user5382: I find that the five Skandhas can be very confusing at times, as the Western idea of mind and perception is very different to the Buddhist idea of mind and perception. On top of that, many explanations of the five Skandhas online seem vague and sometimes seem to be interpreted differently, depending on where you go.
The first Skandha: Form
Does this refer to physical form? Can we only know form through the sense organs?
The second Skandha: Sensation
Are these just sensations from the sense organs?
One description online describes sensation as follows:

... it is the sensation experienced through the contact of eye with
visible form, ear with sound, nose with odor, tongue with taste, body
with tangible things, mind (manas) with ideas or thoughts.

If this is the case, does emotion fall under sensation?
The third Skandha: Perception
A description I found:

Samjna is the faculty that recognizes. Most of what we call thinking fits into the aggregate of samjna.
The word "samjna" means "knowledge that puts together." It is the
capacity to conceptualize and recognize things by associating them
with other things. For example, we recognize shoes as shoes because we
associate them with our previous experience with shoes.

My understanding is that the faculty to recognize is consciousness. However, consciousness is said to be a different Skandha. My understanding is that consciousness is that which perceives the world around it. More broadly, how is perception and consciousness different?
The fourth Skandha: Mental Formation
A description I found:

This aggregate includes all mental factors except feeling and
perception, which are two of the possible fifty-two mental factors
noted in Buddhism.

I'm assuming this is where emotions exist? Is happiness an emotion? Is loving-kindness an emotion? If not, were do they exist, in terms of the Skandhas?
The fifth Skandha: Consciousness
A description I found:

Vijnana is a reaction that has one of the six faculties as its basis and one of the six corresponding phenomena as its object. For example, aural consciousness -- hearing -- has the ear as its basis and a sound as its object. Mental consciousness has the mind (manas) as its basis and an idea or thought as its object.

If this is the case, then is consciousness that which observes sensations, mental formations, perception and form, or that which experiences sensation, perception, mental formations and form? Can the experience of sensation exist if we are not conscious of it? Are animals conscious? Maybe a more important question is: what is the difference between consciousness and self-awareness, in the Buddhist context?
I realize there are a lot of questions here, so thank you to whoever takes the time out of their day to answer them. Have a good day!
Comment: This is a very cogent, very important, even fundamental issue in the process of direct inquiry. The last question haunts me: what is the true definition of consciousness when referred to as a Buddhist skanda? Specifically, self reflexive awareness--for lack of a better term--seems fundamental, even unitary. Vedantic teachings inevitably lead to the direct discovery that "consciousness is all". Consider Turyia. The Tibetan term, Rigpa, seems to point to the same realization.

user10762: Welcome to the world of Buddhism where nothing is clear, everything is totally vague and confusing and where everyone has conflicting and contradictory opinions about how it should be practiced. Some people will tell you there is no right way to meditate, others will tell you you must make sure you are adhering strictly to a technique.

user254: There's an article, The Five Aggregates
(A Study Guide
by
Thanissaro Bhikkhu), which quotes what the Pali suttas say about the aggregates (i.e. the definitions of the aggregates in suttas), for example:

§ 9. Feeling. "And what is feeling? These six bodies of feeling — feeling born of eye-contact, feeling born of ear-contact, feeling born of nose-contact, feeling born of tongue-contact, feeling born of body-contact, feeling born of intellect-contact: this is called feeling."
-- SN 22.57

I could try to define them in my own words but, as you said, "many explanations of the five Skandhas online seem vague and sometimes seem to be interpreted differently, depending on where you go".
Oh well.
I suppose you could read many definitions and try to synthesize them; or read or listen to definitions by reputable teachers.
And/or, there's something called the Abhidharma (which I haven't read): I think the Abhidharma is not Buddhavacana but are a (only slightly later) more elaborate and perhaps more precise description of what various mental phenomena are and how they're related... and so if you want a detailed (or more detailed) description, perhaps (I don't know) you could look into the Abhidharma's description instead of the description implied by the list of Skandhas.

My new theory is as follows: that it's a simple list, into which you shouldn't try to read too much.
There's an article Three Cardinal Discourses of the Buddha: I suppose that (collection of three suttas) is a very high-level summary of the buddhavacana. In the The Not-self Characteristic (Anatta-lakkhana-sutta) uses but doesn't define the list of skandhas. It uses words like "form" and "feeling" without defining them, except to say that they're "not self".
So my theory is that the skandhas are a list of things which a person could possibly view as self (my form, my sense-impressions, my thoughts, etc.), but the purpose of this list is in order to say that these are "not self": so that a person becomes "estranged" from (perhaps instead of "entangled" with) each skandha, and with estrangement is able to become dispassionate and therefore liberated.
IOW it may not exactly matter what the skandhas are and the boundary of each one, how they map to English concepts such as "emotion", or whether a dog has Buddha-nature: what matters (for the purpose of this lesson) is that they're all "not self".

I noticed in this comment you were asking about dukkha. Because I just mentioned "not-self" I should clarify that Buddhism calls these the "three characteristics" (or three facts or three marks) of existence -- i.e. is says that all conditioned things (sankhāra) are impermanent (aniccā), unsatisfactory (dukkhā), and not-self (anattā).
Here is another quote which says that the purpose of analyzing the human being into skandhas is (merely) to show that these things (form, senses, perceptions, etc.) are impermanent:

Although the concept of anicca applies to all compounded and conditioned things, the Buddha is more concerned with the so-called being; for the problem is with man and not with dead things. Like an anatomist who resolves a limb into tissues and tissues into cells, the Buddha, the Analyzer (Vibhajjavaadi), analyzed the so-called being, the sankhaara pu~nja, the heap of processes, into five ever-changing aggregates, and made it clear that there is nothing abiding, nothing eternally conserved, in this conflux of aggregates (khandhaa santati). They are: — — material form or body; feeling or sensation; perception; mental formations; consciousness.
The Enlightened One explains:

The five aggregates, monks, are anicca, impermanent; whatever is impermanent, that is dukkha, unsatisfactory; whatever is dukkha, that is without attaa, self. What is without self, that is not mine, that I am not, that is not my self. Thus should it be seen by perfect wisdom (sammappa~n~naaya) as it really is. Who sees by perfect wisdom, as it really is, his mind, not grasping, is detached from taints; he is liberated.

-- SN 22.45

So the important thing to notice about the skandhas is that they're impermanent (and unsatisfactory and not-self).

user-1: There is a lot of questions in one question. You might consider splitting them up and asking separate questions. This ensures that other users will find it easier to answer the question and you will get better and more precise answers.

My answer is based on the last section of your question, i.e. the part about the 5th aggregate of consciousness.
Consciousness exists a taker of objects. Without consciousness there would be no awareness of the object. 
You might have experienced this before, e.g. if you have been fully absorped in a good book or movie and someone calls your name and you dont hear it. That is not because the sound of the voice is not there, its just because consciousness was not at the ear-sensebase at that moment.
There are 3 factors that must come together in order to talk about conscious experience. 

The sense base, e.g. The eye-sensebase.
Visible light which is the corresponding object for the eye
Eye consciousness

Consciousness is further divided into the 6 types according to it's bases:

Eye consciousness cognizes light, i.e. visible forms and objects.
Ear consciousness cognizes sound
Nose consciousness cognizes smell
Tongue consciousness cognizes taste
Body consciousness cognizes tangible sensations
Mind consciousness cognizes mental objects such as ideas, concepts, thoughts, volitions and other mental formations

To gain more knowledge about this i would recommend listening to this dhamma talk on the 5 aggregates by Ven. Bhikkhu Bodhi. This talk gives a detailed explanation of all the aggregates.

user111: Rupa

Does this refer to physical form? 

Yes, anything physical is included in this category. Ex: light, sound, aromas,earth element, water element, heat element, air element  etc. 
However, with regards to the five skandhas, a thought is also called a rupa when it becomes the object received by the mind sense faculty. Ex: a memory

Can we only know form through the sense organs?

Yes, there'll be no knowing without the 6 senses.
Vedana

Are these just sensations from the sense organs?

Sense organs cannot produce sensation by themselves. The contact should occur. That is the union of Rupa, sense organ and the relevant consciousness.
ex: light, eye and the eye consciousness 
There are basically 3 kinds of sensations: pleasant, painful and neutral.

If this is the case, does emotion fall under sensation?

No, that is Sankhara(Mental Formation).
Sanna(Perception)

My understanding is that the faculty to recognize is consciousness

No. Consciousness is just base awareness.

how is perception and consciousness different?

Sanna(perception) is what recognizes the object specifically. Awareness cannot tell what it is. But awareness is present at this stage as they all rise together. 
Sankhara(Mental Formation)

I'm assuming this is where emotions exist? Is happiness an emotion? Is
  loving-kindness an emotion?

Yes, that's right. Happiness, loving kindness, hatred, jealousy, craving etc. belong to this group
Vinnana(Consciousness)

If this is the case, then is consciousness that which observes
  sensations, mental formations, perception and form, or that which
  experiences sensation, perception, mental formations and form?

A single experience contains all 5 of the Skhandas. They make up the whole experience. Think of it as drinking a chocolate milk shake. When you drink it, do you feel the taste of milk, chocolate, sugar separately? No. You feel them all together. Consciousness is like the water they are all mixed in. Consciousness cannot separately observe anything. Observing itself is an experience where all 5 skandhas are present.  In an experience, consciousness simply plays the role of being aware. When you are asleep, the ear consciousness may not be present at the ears. That's why you won't be able to hear, even if the sound hits the ears.

Can the experience of sensation exist if we are not conscious of it?

No. Every experience has all the 5 skhandas. 

Are animals conscious?

Yes, they are beings. It's Panchaskhandha for them as well

what is the difference between consciousness and self-awareness?

Consciousness is what plays the role of being aware in an experience. Self-awareness is an experience(5 skandhas) in which the perception identifies the object of the experience as a self.   
To give a common example to illustrate the functions of the Skandhas, say you are smelling something delicious. The smell and the nose here are Rupa. When they get together with the nose consciousness, contact happens. At that moment the Vinnana is aware that an object is present at the nose sense door. Vedana tells that it is pleasant. Sanna tells what it is: whether it's a pudding, cake, ice cream etc. Sankhara tells it's good and desires for it. Keep in mind that the event of smelling here involves many instances of five aggregates rising and passing away.  

5382: <p>I find that the five Skandhas can be very confusing at times, as the Western idea of mind and perception is very different to the Buddhist idea of mind and perception. On top of that, many explanations of the five Skandhas online seem vague and sometimes seem to be interpreted differently, depending on where you go.</p>
<h2>The first Skandha: <strong>Form</strong></h2>
<p>Does this refer to physical form? Can we only know form through the sense organs?</p>
<h2>The second Skandha: <strong>Sensation</strong></h2>
<p>Are these just sensations from the sense organs?</p>
<p>One description online describes sensation as follows:</p>
<blockquote>
<p>... it is the sensation experienced through the contact of eye with
visible form, ear with sound, nose with odor, tongue with taste, body
with tangible things, mind (manas) with ideas or thoughts.</p>
</blockquote>
<p>If this is the case, does emotion fall under sensation?</p>
<h2>The third Skandha: <strong>Perception</strong></h2>
<p>A description I found:</p>
<blockquote>
<p>Samjna is the faculty that recognizes. Most of what we call thinking fits into the aggregate of samjna.</p>
<p>The word &quot;samjna&quot; means &quot;knowledge that puts together.&quot; It is the
capacity to conceptualize and recognize things by associating them
with other things. For example, we recognize shoes as shoes because we
associate them with our previous experience with shoes.</p>
</blockquote>
<p>My understanding is that the faculty to recognize is consciousness. However, consciousness is said to be a different Skandha. My understanding is that consciousness is that which perceives the world around it. More broadly, how is perception and consciousness different?</p>
<h2>The fourth Skandha: <strong>Mental Formation</strong></h2>
<p>A description I found:</p>
<blockquote>
<p>This aggregate includes all mental factors except feeling and
perception, which are two of the possible fifty-two mental factors
noted in Buddhism.</p>
</blockquote>
<p>I'm assuming this is where emotions exist? Is happiness an emotion? Is loving-kindness an emotion? If not, were do they exist, in terms of the Skandhas?</p>
<h2>The fifth Skandha: <strong>Consciousness</strong></h2>
<p>A description I found:</p>
<blockquote>
<p>Vijnana is a reaction that has one of the six faculties as its basis and one of the six corresponding phenomena as its object. For example, aural consciousness -- hearing -- has the ear as its basis and a sound as its object. Mental consciousness has the mind (manas) as its basis and an idea or thought as its object.</p>
</blockquote>
<p>If this is the case, then is consciousness that which <em>observes</em> sensations, mental formations, perception and form, or that which <em>experiences</em> sensation, perception, mental formations and form? Can the experience of sensation exist if we are not conscious of it? Are animals conscious? Maybe a more important question is: what is the difference between consciousness and self-awareness, in the Buddhist context?</p>
<p>I realize there are a lot of questions here, so thank you to whoever takes the time out of their day to answer them. Have a good day!</p>
<p>Comment: This is a very cogent, very important, even fundamental issue in the process of direct inquiry. The last question haunts me: what is the true definition of consciousness when referred to as a Buddhist skanda? Specifically, self reflexive awareness--for lack of a better term--seems fundamental, even unitary. Vedantic teachings inevitably lead to the direct discovery that &quot;consciousness is all&quot;. Consider Turyia. The Tibetan term, Rigpa, seems to point to the same realization.</p>
 10762: <p>Welcome to the world of Buddhism where nothing is clear, everything is totally vague and confusing and where everyone has conflicting and contradictory opinions about how it should be practiced. Some people will tell you there is no right way to meditate, others will tell you you must make sure you are adhering strictly to a technique.</p>
 254: <p>There's an article, <a href="http://www.accesstoinsight.org/lib/study/khandha.html" rel="nofollow noreferrer">The Five Aggregates
(A Study Guide
by
Thanissaro Bhikkhu)</a>, which quotes what the Pali suttas say about the aggregates (i.e. the definitions of the aggregates in suttas), for example:</p>
<blockquote>
<p>§ 9. Feeling. &quot;And what is feeling? These six bodies of feeling — feeling born of eye-contact, feeling born of ear-contact, feeling born of nose-contact, feeling born of tongue-contact, feeling born of body-contact, feeling born of intellect-contact: this is called feeling.&quot;</p>
<p>-- <a href="http://www.accesstoinsight.org/tipitaka/sn/sn22/sn22.057.than.html" rel="nofollow noreferrer">SN 22.57</a></p>
</blockquote>
<p>I could try to define them in my own words but, as you said, &quot;many explanations of the five Skandhas online seem vague and sometimes seem to be interpreted differently, depending on where you go&quot;.</p>
<p>Oh well.</p>
<p>I suppose you could read many definitions and try to synthesize them; or read or listen to definitions by reputable teachers.</p>
<p>And/or, there's something called the <a href="https://en.wikipedia.org/wiki/Abhidharma" rel="nofollow noreferrer">Abhidharma</a> (which I haven't read): I think the Abhidharma is not <a href="https://en.wikipedia.org/wiki/Buddhavacana" rel="nofollow noreferrer">Buddhavacana</a> but are a (only slightly later) more elaborate and perhaps more precise description of what various mental phenomena are and how they're related... and so if you want a detailed (or more detailed) description, perhaps (I don't know) you could look into the Abhidharma's description instead of the description implied by the list of Skandhas.</p>
<hr />
<p>My new theory is as follows: that it's a simple list, into which you shouldn't try to read too much.</p>
<p>There's an article <a href="http://www.accesstoinsight.org/lib/authors/nanamoli/wheel017.html" rel="nofollow noreferrer">Three Cardinal Discourses of the Buddha</a>: I suppose that (collection of three suttas) is a very high-level summary of the buddhavacana. In the <em>The Not-self Characteristic (Anatta-lakkhana-sutta)</em> uses but doesn't define the list of skandhas. It uses words like &quot;form&quot; and &quot;feeling&quot; without defining them, except to say that they're &quot;not self&quot;.</p>
<p>So my theory is that the skandhas are a list of things which a person could possibly view as self (my form, my sense-impressions, my thoughts, etc.), but the purpose of this list is in order to say that these are &quot;not self&quot;: so that a person becomes &quot;estranged&quot; from (perhaps instead of &quot;entangled&quot; with) each skandha, and with estrangement is able to become dispassionate and therefore liberated.</p>
<p>IOW it may not exactly matter what the skandhas are and the boundary of each one, how they map to English concepts such as &quot;emotion&quot;, or whether a dog has Buddha-nature: what matters (for the purpose of this lesson) is that they're all &quot;not self&quot;.</p>
<hr />
<p>I noticed in <a href="https://buddhism.stackexchange.com/questions/9963/three-questions-about-sensual-desire/9980#comment14338_9980">this comment</a> you were asking about <em>dukkha</em>. Because I just mentioned &quot;not-self&quot; I should clarify that Buddhism calls these the &quot;three characteristics&quot; (or three facts or three marks) of existence -- i.e. is says that all conditioned things (<em>sankhāra</em>) are impermanent (<em>aniccā</em>), unsatisfactory (dukkhā), and not-self (<em>anattā</em>).</p>
<p><a href="http://www.accesstoinsight.org/lib/authors/various/wheel186.html" rel="nofollow noreferrer">Here is another quote</a> which says that the purpose of analyzing the human being into skandhas is (merely) to show that these things (form, senses, perceptions, etc.) are impermanent:</p>
<blockquote>
<p>Although the concept of <em>anicca</em> applies to all compounded and conditioned things, the Buddha is more concerned with the so-called being; for the problem is with man and not with dead things. Like an anatomist who resolves a limb into tissues and tissues into cells, the Buddha, the Analyzer (<em>Vibhajjavaadi</em>), analyzed the so-called being, the <em>sankhaara pu~nja</em>, the heap of processes, into five ever-changing aggregates, and made it clear that there is nothing abiding, nothing eternally conserved, in this conflux of aggregates (<em>khandhaa santati</em>). They are: — — material form or body; feeling or sensation; perception; mental formations; consciousness.</p>
<p>The Enlightened One explains:</p>
<blockquote>
<p>The five aggregates, monks, are <em>anicca</em>, impermanent; whatever is impermanent, that is <em>dukkha</em>, unsatisfactory; whatever is <em>dukkha</em>, that is without <em>attaa</em>, self. What is without self, that is not mine, that I am not, that is not my self. Thus should it be seen by perfect wisdom (<em>sammappa~n~naaya</em>) as it really is. Who sees by perfect wisdom, as it really is, his mind, not grasping, is detached from taints; he is liberated.</p>
</blockquote>
<p>-- SN 22.45</p>
</blockquote>
<p>So the important thing to notice about the skandhas is that they're impermanent (and unsatisfactory and not-self).</p>
 -1: <p>There is a lot of questions in one question. You might consider splitting them up and asking separate questions. This ensures that other users will find it easier to answer the question and you will get better and more precise answers.</p>

<hr>

<p>My answer is based on the last section of your question, i.e. the part about the <em>5th aggregate of consciousness</em>.</p>

<p>Consciousness exists a taker of objects. Without consciousness there would be no awareness of the object. </p>

<p>You might have experienced this before, e.g. if you have been fully absorped in a good book or movie and someone calls your name and you dont hear it. That is not because the sound of the voice is not there, its just because consciousness was not at the ear-sensebase at that moment.</p>

<p>There are 3 factors that must come together in order to talk about <em>conscious experience</em>. </p>

<ol>
<li>The sense base, e.g. The eye-sensebase.</li>
<li>Visible light which is the corresponding object for the eye</li>
<li>Eye consciousness</li>
</ol>

<p>Consciousness is further divided into the 6 types according to it's bases:</p>

<ul>
<li><p>Eye consciousness cognizes light, i.e. visible forms and objects.</p></li>
<li><p>Ear consciousness cognizes sound</p></li>
<li><p>Nose consciousness cognizes smell</p></li>
<li><p>Tongue consciousness cognizes taste</p></li>
<li><p>Body consciousness cognizes tangible sensations</p></li>
<li><p>Mind consciousness cognizes mental objects such as ideas, concepts, thoughts, volitions and other mental formations</p></li>
</ul>

<p><a href="http://www.noblepath.org/BB/20131005MN109-a.mp3" rel="noreferrer">To gain more knowledge about this i would recommend listening to this dhamma talk on the 5 aggregates by Ven. Bhikkhu Bodhi</a>. This talk gives a detailed explanation of all the aggregates.</p>
 111: <p><a href="http://www.accesstoinsight.org/lib/authors/mendis/wheel322.html#ruupa" rel="noreferrer"><strong>Rupa</strong></a></p>

<blockquote>
  <p>Does this refer to physical form? </p>
</blockquote>

<p>Yes, anything physical is included in this category. Ex: light, sound, aromas,earth element, water element, heat element, air element  etc. 
However, with regards to the five skandhas, a thought is also called a rupa when it becomes the object received by the mind sense faculty. Ex: a memory</p>

<blockquote>
  <p>Can we only know form through the sense organs?</p>
</blockquote>

<p>Yes, there'll be no knowing without the 6 senses.</p>

<p><strong><a href="http://www.beyondthenet.net/dhamma/feelings.htm" rel="noreferrer">Vedana</a></strong></p>

<blockquote>
  <p>Are these just sensations from the sense organs?</p>
</blockquote>

<p>Sense organs cannot produce sensation by themselves. The contact should occur. That is the union of Rupa, sense organ and the relevant consciousness.
ex: light, eye and the eye consciousness </p>

<p>There are basically 3 kinds of sensations: pleasant, painful and neutral.</p>

<blockquote>
  <p>If this is the case, does emotion fall under sensation?</p>
</blockquote>

<p>No, that is Sankhara(Mental Formation).</p>

<p><strong><a href="http://www.beyondthenet.net/dhamma/perceptions.htm" rel="noreferrer">Sanna(Perception)</a></strong></p>

<blockquote>
  <p>My understanding is that the faculty to recognize is consciousness</p>
</blockquote>

<p>No. Consciousness is just base awareness.</p>

<blockquote>
  <p>how is perception and consciousness different?</p>
</blockquote>

<p>Sanna(perception) is what recognizes the object specifically. Awareness cannot tell what it is. But awareness is present at this stage as they all rise together. </p>

<p><strong><a href="http://www.beyondthenet.net/dhamma/formations.htm" rel="noreferrer">Sankhara(Mental Formation)</a></strong></p>

<blockquote>
  <p>I'm assuming this is where emotions exist? Is happiness an emotion? Is
  loving-kindness an emotion?</p>
</blockquote>

<p>Yes, that's right. Happiness, loving kindness, hatred, jealousy, craving etc. belong to this group</p>

<p><a href="http://www.beyondthenet.net/dhamma/consciousness.htm" rel="noreferrer"><strong>Vinnana(Consciousness)</strong></a></p>

<blockquote>
  <p>If this is the case, then is consciousness that which observes
  sensations, mental formations, perception and form, or that which
  experiences sensation, perception, mental formations and form?</p>
</blockquote>

<p>A single experience contains all 5 of the Skhandas. They make up the whole experience. Think of it as drinking a chocolate milk shake. When you drink it, do you feel the taste of milk, chocolate, sugar separately? No. You feel them all together. Consciousness is like the water they are all mixed in. Consciousness cannot separately observe anything. Observing itself is an experience where all 5 skandhas are present.  In an experience, consciousness simply plays the role of being aware. When you are asleep, the ear consciousness may not be present at the ears. That's why you won't be able to hear, even if the sound hits the ears.</p>

<blockquote>
  <p>Can the experience of sensation exist if we are not conscious of it?</p>
</blockquote>

<p>No. Every experience has all the 5 skhandas. </p>

<blockquote>
  <p>Are animals conscious?</p>
</blockquote>

<p>Yes, they are beings. It's Panchaskhandha for them as well</p>

<blockquote>
  <p>what is the difference between consciousness and self-awareness?</p>
</blockquote>

<p>Consciousness is what plays the role of being aware in an experience. Self-awareness is an experience(5 skandhas) in which the perception identifies the object of the experience as a self.   </p>

<p>To give a common example to illustrate the functions of the Skandhas, say you are smelling something delicious. The smell and the nose here are Rupa. When they get together with the nose consciousness, contact happens. At that moment the Vinnana is aware that an object is present at the nose sense door. Vedana tells that it is pleasant. Sanna tells what it is: whether it's a pudding, cake, ice cream etc. Sankhara tells it's good and desires for it. Keep in mind that the event of smelling here involves many instances of five aggregates rising and passing away.  </p>
