user18120: Suppose I have a mirror, or a picture on the wall, and I want to run a second video into this. 
How could that be achieved? And even in such a way as to correct for perspective?
For example, like in this video.

user5546: This can easily be accomplished using the "picture-in-picture" feature of most editing software. I've used Adobe Premiere and iMovie, and both include that feature.  Premiere has the advantage that you can "mask" a layer, so it is not quite rectangular, in order to fit the shape of the mirror.
Make sure the camera for the main scene is on a tripod and does not move at all. If that camera moves, you will need to animate your picture-in-picture video and mask so it appears to stay inside the mirror's frame.

user6207: If you can use a tool like Apple's Motion or FCPX, or Adobe's After Effects, they all have the ability to put the 4 corners of a layer anywhere you want. With Motion or After Effects, you can even track the 4 corners and keep the "TV" image pinned in the right place.
In Motion, you can select a clip and open the Inspector. In the Inspector, press the "Properties" tab. There's a section in the properties called "Four Corner". If you twirl that open, it allows you to set where the 4 corners of the video go. You can put them wherever you like.
FCPX is similar - select the clip, and open the inspector. There should be a section in the inspector named "Distort". This will also let you set the 4 corners of the clip.
In After Effects you can select a layer and apply the built-in "Corner Pin" effect.

18120: <p>Suppose I have a mirror, or a picture on the wall, and I want to run a second video into this. </p>

<p>How could that be achieved? And even in such a way as to correct for perspective?</p>

<p>For example, like in <a href="https://www.youtube.com/watch?v=7i3DxuyTQbU#t=4m14s" rel="nofollow noreferrer">this video</a>.</p>
 5546: <p>This can easily be accomplished using the "picture-in-picture" feature of most editing software. I've used Adobe Premiere and iMovie, and both include that feature.  Premiere has the advantage that you can "mask" a layer, so it is not quite rectangular, in order to fit the shape of the mirror.</p>

<p>Make sure the camera for the main scene is on a tripod and does not move at all. If that camera moves, you will need to animate your picture-in-picture video and mask so it appears to stay inside the mirror's frame.</p>
 6207: <p>If you can use a tool like Apple's Motion or FCPX, or Adobe's After Effects, they all have the ability to put the 4 corners of a layer anywhere you want. With Motion or After Effects, you can even track the 4 corners and keep the "TV" image pinned in the right place.</p>

<p>In <a href="https://help.apple.com/motion/mac/5.3/" rel="nofollow noreferrer">Motion</a>, you can select a clip and open the Inspector. In the Inspector, press the "Properties" tab. There's a section in the properties called "Four Corner". If you twirl that open, it allows you to set where the 4 corners of the video go. You can put them wherever you like.</p>

<p><a href="https://help.apple.com/finalcutpro/mac/10.3/" rel="nofollow noreferrer">FCPX</a> is similar - select the clip, and open the inspector. There should be a section in the inspector named "Distort". This will also let you set the 4 corners of the clip.</p>

<p>In <a href="https://helpx.adobe.com/after-effects/using/layer-properties.html" rel="nofollow noreferrer">After Effects</a> you can select a layer and apply the built-in "Corner Pin" effect.</p>
