That is an interesting question.
First, we are all familiar with a flat mirror. Light hits a mirror and bounces back so that we can see the "reflection." A flat mirror will do this fairly accurately, depending on the quality of the mirror.
A concave mirror is not flat; it bulges away from the light (kind of like if you nailed a bowl to the wall with the part you'd put your soup in facing you.) These types of mirrors tend to focus light toward the inner center. The image shown, then, is very different depending on where you are standing in proximity to the mirror. Common uses are in automobile headlights and searchlights, which can focus light in one direction.
A convex mirror is the opposite. It is the bowl nailed to the wall so that the part that holds the soup is not facing you. These types of mirrors tend to spread out light instead of concentrating it. They are sometimes called "fish eyes" and can give the person looking into the mirror a wide field of vision. An example of the use of such a mirror would be on ATM machines that allow the person punching in their password to see all the nefarious individuals behind them ready to pounce on them once the $20 comes out.
Both, by construction, are spherical in form (would turn into a ball if the mirror were "finished".) Most of these mirrors are "cut in half" for our use (besides the ubiquitous disco ball, but I don't know if that really counts as a mirror.)
The major disadvantage is the distortion of the image. The wider the "aperture" of the mirror the more distorting it is going to be on the image.