Curved mirrors combine the behavior of a flat mirror and a lens.

Concave mirrors are like positive (convex) lenses, in that they bring parallel beams of light together at a single point, called the focal point or focus. 
Notice in the picture how relected light from a curved mirror still follows the same rule that we discovered with flat mirrors - that the angle of the reflected light beam relative to the mirror, is the same as the angle of the incident beam (the beam that comes into the mirror).  Or more simply,  the angle in equals the angle out.   A curved mirror differs from a flat mirror in that the surface itself is tilted in different directions at different places.
Concave mirrors are also like positive lenses in that they are magnifying mirrors, giving upright images if you look at them from close up, while they give an inverted reflection if you look at them from far enough away.

Convex mirrors are like negative (concave) lenses -- they make parallel beams of light diverge, and make your reflected image smaller. But this makes room within the view for reflections of other things, and so they give a "wide angle" view.

This person can see a star, a flower, himself, and the grass, all reflected at once in the convex mirror.
Your image in a flat mirror is the same size as yourself, and its apparent location is just as far beyond the mirror surface as you are in front of it. With curved mirrors there is still an image, generally, but its size and position will be different.
Because a curved mirror is a mirror, the beams coming in pass through the beams coming out, which makes it harder to use them for optical instruments. On the other hand, they are easy to design and make (since there is only one surface at which something happens), and they treat all wavelengths of light the same (whereas all lenses are slightly wavelength dependent, so that images of a white object tend to have colored edges). Thus they are used in astronomical telescopes and some other applications where the optical system needs to be of extremely high quality.
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What have we learned about curved mirrors?