user57: In this question How to help non-Buddhists understand a young person's desire to be ordained as a monk?, one of the "selling points" listed was:

5) Supernatural mental abilities (astral travel, reading minds, remembering past lives, etc.)

Could someone explain this is more detail? I had thought this was more of a pop culture point rather than what seems to be a core concept.  
Do such "abilities" actually exist, and if so what is their implication in the practice of Buddhism or proceeding in one's daily life? Do monks or others actively practice them?

user67: 
Thomas [Aquinas] defined a miracle as "whatever God does outside and beyond the order commonly determined or observed in nature". Buddhism would agree with this definition except that it would replace the word 'God' with the word 'mind'. The development and purification of the mind through ethical and meditational training can unleash powers not normally apparent which would usually be described as miraculous. The miraculous powers (abhinna iddhi / siddhi) often mentioned in the Buddhist scriptures, and sometimes manifested by the Buddha himself, include being able to multiply oneself, fly through the air, hear things over a long distance, read other people's minds, remember one's former lives and know how to destroy the defilements of the mind. Only the last three of these is considered to be important. There is little doubt that the Buddha had a cautious attitude to these and other miraculous powers. He pointed out that they could simply be due to magic or fraud rather than genuine spiritual accomplishments. 

Source: "Dharma Data: Miracles" at BuddhaNet
When asked to perform a miracle in order to impress and thereby convert people, he refused saying that education was the greatest of miracles. So from the Buddhist perspective, the ability to perform miracles is not proof of holiness and it need not have a spiritual value although it may be used for the benefit of others. 

The Buddha's Attitude to Miracles
Miracles of Gautama Buddha on Wikipedia


user7611: Superhuman abilities are described many times in the suttas like the Iddhipada-vibhanga Sutta and many others.
Of course they are real and not metaphors or vain myths. But there are many other abilities outside the basic categorizations (as mentioned by The Buddha himself). 
Once one achieves a certain level of concentration they can experience all types of superhuman abilities. They are categorized in a certain manner in the Pali canons called the "six higher knowledges" or "Abhijñā".
I saw a documentary a long time ago, called something like "The KGB Paranormal Files" about the Soviet Union researching psychic powers encountering Tibetan monks rumored to have all types of psychic powers. They did experiments with some monks and asked them to concentrate on breaking a skull and within moments it really happened. I found the video, here it is https://www.youtube.com/watch?v=_CH0VyYbwuk&feature=youtu.be&t=3741. 
For me personally I've only experienced subtle powers like sometimes knowing the minds and perceptions of others, healing myself, and experiencing extreme enjoyment from the destruction of asavas. 
I know that with practice almost anyone who develops concentration would be able to achieve superhuman powers with little difficulty, it's not as a hard as it seems. With proper training it would probably only takes months or less of practice.
But I'm not very interested in developing superhuman abilities right now because it seems unnecessary and not useful to me given my current state. 
I'm only interested in the ending of mental fermentations (asavas) because it's very useful to me to experience such enjoyment and put an end to the perpetual cycle of misery. 
The thought arose in my mind "What is the point in having all types of superhuman abilities if one still experiences fear, anger, sorrow, boredom, and other miserable states?". With the destruction of asavas I would experience extreme enjoyment, stand fearless, doubtless, sorrowless, just enjoying this eternal moment. So what greater power could there be?
Right now I'm focusing on developing mind-exercises to end mental fermentations (asavas) since exact precise methods seem to have either completely disappeared or are hidden well during this time-period. All that's leftover now in modern times are vague teachings and ideas, not exact precise methods. I hope to become an arahant or paccekabuddha in this existence.
After that achievement I would be able to develop other superhuman abilities easily if I wanted.
Here are some of my personal experiences:

I concentrate on healing myself, after a few seconds or minutes of concentration I feel tingling vibrations coming out of my body, my nose becomes unstuffed, my vision improves slightly, and my overall health improves
I concentrate on destroying painful feelings inside of me, I see that in the past I insulted others harshly which is one of the vain trifling deeds holding me back
I concentrate on destroying painful feelings inside of me, I feel a type of energy go into my forehead third eye area and experience bliss, I try harder and the energy goes above my third eye to the top of my head and experience such an extreme form of enjoyment that I see no other greater pleasure

I also believe that in the past I practiced mind-exercises in early pre-ancient Egypt a long long time ago, which unconsciously unknowingly I revived now in modern times. It seems that the earlier Egyptians were highly interested in mind-exercises and meditation, many from that time are now here during this time-period. Also sometimes I see spirits of deceased relatives, heavenly and hellish beings.
Certainly this extreme form of enjoyment is the greatest gain, greatest pleasure, the only noteworthy goal in life.

user43: In my opinion, supernatural abilities are metaphors for various mental/psychological skills. This seems to accord well with Chogyam Trungpa's interpretation of Six Worlds as psychological states, and his other teachings.
Reading minds is a metaphor for a highly refined ability to read person's hidden intentions/judgements from context, background info, and non-verbal queues.
Remembering past lives is a metaphor for clearly understanding the patterns of behavior that carry on from generation to generation.
So-called Heavenly Eye is a metaphor for being able to see things objectively, without a personal bias.
Ancients were rather rational people, but they had their way of talking about things, which may look weird to a modern person.

user32: The question is slightly broad and asks about several different facets.  I'm going to focus on "Do monks or others actively practice them?"  The answer to this is "yes, some do."
There are a variety of beliefs and practices in a wide array of different Buddhist traditions which could be considered to be "Supernatural" in some way, shape, or form. They could also be considered wholly "natural" depending on your point of view of the mechanics behind what is happening. 
There are practices such as tummo which have received some amount of study that allow for increasing the core body temperature.  This may or may not count as "supernatural" but it would certainly seem that way to an outside observer with no experience in the practice. 
There is a belief among some practitioners of certain sects that there is a literal rainbow body phenomena wherein the body releases light and, sometimes, shrinks (my source on this is a conversation with a monk, if someone knows of something written down I'd be interested).  It is believed that this can be attained through the practice of dzogchen.
Information on belief in various forms of an "energy body" or "subtle body" are everywhere in various Buddhist traditions. 
There's a practice called dream yoga which includes something that could very well be considered "astral travel," though it is notoriously difficult to take a classification system derived from one system and apply it to another, so whether you count it as "astral," "illusory," or "supernatural" or just something related to what others call that may be tricky. These practices certainly have been used historically for divination (as described by Tenzin Wangyal Rinpoche), among other purposes. 
This isn't even getting into the phenomena of emanations and other such beliefs.
Basically: There are certainly beliefs and practices, engaged in by both monks and non-monks, that can be interpreted this way.

57: <p>In this question <a href="https://buddhism.stackexchange.com/questions/137/how-to-help-non-buddhists-understand-a-young-persons-desire-to-be-ordained-as-a">How to help non-Buddhists understand a young person's desire to be ordained as a monk?</a>, one of the "selling points" listed was:</p>

<blockquote>
  <p>5) Supernatural mental abilities (astral travel, reading minds, remembering past lives, etc.)</p>
</blockquote>

<p>Could someone explain this is more detail? I had thought this was more of a pop culture point rather than what seems to be a core concept.  </p>

<p>Do such "abilities" actually exist, and if so what is their implication in the practice of Buddhism or proceeding in one's daily life? Do monks or others actively practice them?</p>
 67: <blockquote>
  <p>Thomas [Aquinas] defined a miracle as "whatever God does outside and beyond the order commonly determined or observed in nature". Buddhism would agree with this definition except that it would replace the word 'God' with the word 'mind'. The development and purification of the mind through ethical and meditational training can unleash powers not normally apparent which would usually be described as miraculous. The miraculous powers (<em>abhinna iddhi</em> / <em>siddhi</em>) often mentioned in the Buddhist scriptures, and sometimes manifested by the Buddha himself, include being able to multiply oneself, fly through the air, hear things over a long distance, read other people's minds, remember one's former lives and know how to destroy the defilements of the mind. Only the last three of these is considered to be important. There is little doubt that the Buddha had a cautious attitude to these and other miraculous powers. He pointed out that they could simply be due to magic or fraud rather than genuine spiritual accomplishments. </p>
</blockquote>

<p>Source: <a href="http://www.buddhanet.net/e-learning/dharmadata/fdd63.htm" rel="nofollow">"Dharma Data: Miracles" at BuddhaNet</a></p>

<p>When asked to perform a miracle in order to impress and thereby convert people, he refused saying that <strong>education was the greatest of miracles</strong>. So from the Buddhist perspective, the ability to perform miracles is not proof of holiness and it need not have a spiritual value although it may be used for the benefit of others. </p>

<ul>
<li><a href="http://www.buddhanet.net/e-learning/buddhism/lifebuddha/2_26lbud.htm" rel="nofollow">The Buddha's Attitude to Miracles</a></li>
<li><a href="https://en.wikipedia.org/wiki/Miracles_of_Gautama_Buddha" rel="nofollow">Miracles of Gautama Buddha</a> on Wikipedia</li>
</ul>
 7611: <p>Superhuman abilities are described many times in the suttas like the Iddhipada-vibhanga Sutta and many others.</p>

<p>Of course they are real and not metaphors or vain myths. But there are many other abilities outside the basic categorizations (as mentioned by The Buddha himself). </p>

<p>Once one achieves a certain level of concentration they can experience all types of superhuman abilities. They are categorized in a certain manner in the Pali canons called the "six higher knowledges" or "Abhijñā".</p>

<p>I saw a documentary a long time ago, called something like "The KGB Paranormal Files" about the Soviet Union researching psychic powers encountering Tibetan monks rumored to have all types of psychic powers. They did experiments with some monks and asked them to concentrate on breaking a skull and within moments it really happened. I found the video, here it is <a href="https://www.youtube.com/watch?v=_CH0VyYbwuk&amp;feature=youtu.be&amp;t=3741" rel="nofollow">https://www.youtube.com/watch?v=_CH0VyYbwuk&amp;feature=youtu.be&amp;t=3741</a>. </p>

<p>For me personally I've only experienced subtle powers like sometimes knowing the minds and perceptions of others, healing myself, and experiencing extreme enjoyment from the destruction of asavas. </p>

<p>I know that with practice almost anyone who develops concentration would be able to achieve superhuman powers with little difficulty, it's not as a hard as it seems. With proper training it would probably only takes months or less of practice.</p>

<p>But I'm not very interested in developing superhuman abilities right now because it seems unnecessary and not useful to me given my current state. </p>

<p>I'm only interested in the ending of mental fermentations (asavas) because it's very useful to me to experience such enjoyment and put an end to the perpetual cycle of misery. </p>

<p>The thought arose in my mind "What is the point in having all types of superhuman abilities if one still experiences fear, anger, sorrow, boredom, and other miserable states?". With the destruction of asavas I would experience extreme enjoyment, stand fearless, doubtless, sorrowless, just enjoying this eternal moment. So what greater power could there be?</p>

<p>Right now I'm focusing on developing mind-exercises to end mental fermentations (asavas) since exact precise methods seem to have either completely disappeared or are hidden well during this time-period. All that's leftover now in modern times are vague teachings and ideas, not exact precise methods. I hope to become an arahant or paccekabuddha in this existence.</p>

<p>After that achievement I would be able to develop other superhuman abilities easily if I wanted.</p>

<p>Here are some of my personal experiences:</p>

<ul>
<li>I concentrate on healing myself, after a few seconds or minutes of concentration I feel tingling vibrations coming out of my body, my nose becomes unstuffed, my vision improves slightly, and my overall health improves</li>
<li>I concentrate on destroying painful feelings inside of me, I see that in the past I insulted others harshly which is one of the vain trifling deeds holding me back</li>
<li>I concentrate on destroying painful feelings inside of me, I feel a type of energy go into my forehead third eye area and experience bliss, I try harder and the energy goes above my third eye to the top of my head and experience such an extreme form of enjoyment that I see no other greater pleasure</li>
</ul>

<p>I also believe that in the past I practiced mind-exercises in early pre-ancient Egypt a long long time ago, which unconsciously unknowingly I revived now in modern times. It seems that the earlier Egyptians were highly interested in mind-exercises and meditation, many from that time are now here during this time-period. Also sometimes I see spirits of deceased relatives, heavenly and hellish beings.</p>

<p>Certainly this extreme form of enjoyment is the greatest gain, greatest pleasure, the only noteworthy goal in life.</p>
 43: <p>In my opinion, supernatural abilities are metaphors for various mental/psychological skills. This seems to accord well with Chogyam Trungpa's interpretation of Six Worlds as psychological states, and his other teachings.</p>

<p>Reading minds is a metaphor for a highly refined ability to read person's hidden intentions/judgements from context, background info, and non-verbal queues.</p>

<p>Remembering past lives is a metaphor for clearly understanding the patterns of behavior that carry on from generation to generation.</p>

<p>So-called Heavenly Eye is a metaphor for being able to see things objectively, without a personal bias.</p>

<p>Ancients were rather rational people, but they had their way of talking about things, which may look weird to a modern person.</p>
 32: <p>The question is slightly broad and asks about several different facets.  I'm going to focus on "Do monks or others actively practice them?"  The answer to this is "yes, some do."</p>

<p>There are a variety of beliefs and practices in a wide array of different Buddhist traditions which could be considered to be "Supernatural" in some way, shape, or form. They could also be considered wholly "natural" depending on your point of view of the mechanics behind what is happening. </p>

<p>There are practices such as <em>tummo</em> which have received <a href="http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0058244" rel="nofollow">some amount of study</a> that allow for increasing the core body temperature.  This may or may not count as "supernatural" but it would certainly seem that way to an outside observer with no experience in the practice. </p>

<p>There is a belief among some practitioners of certain sects that there is a literal <a href="http://en.wikipedia.org/wiki/Rainbow_body" rel="nofollow">rainbow body phenomena</a> wherein the body releases light and, sometimes, shrinks (my source on this is a conversation with a monk, if someone knows of something written down I'd be interested).  It is believed that this can be attained through the practice of <em>dzogchen</em>.</p>

<p>Information on belief in various forms of an "energy body" or "subtle body" are everywhere in various Buddhist traditions. </p>

<p>There's a practice called <a href="http://en.wikipedia.org/wiki/Dream_yoga" rel="nofollow">dream yoga</a> which includes something that could very well be considered "astral travel," though it is notoriously difficult to take a classification system derived from one system and apply it to another, so whether you count it as "astral," "illusory," or "supernatural" or just something related to what others call that may be tricky. These practices certainly have been used historically for divination (as described by Tenzin Wangyal Rinpoche), among other purposes. </p>

<p>This isn't even getting into the phenomena of <a href="http://en.wikipedia.org/wiki/Tulku" rel="nofollow">emanations</a> and other such beliefs.</p>

<p>Basically: There are certainly beliefs and practices, engaged in by both monks and non-monks, that can be interpreted this way.</p>
