How does mip-mapping work with non-power-of-2 textures? I have heard that recent GPUs all support non-power-of-2 textures and all features just work. However, I don't understand how mip-mapping would work in such a scenario. Can someone explain?
The rule is that to compute the next mipmap size, you divide by two and round down to the nearest integer (unless it rounds down to 0, in which case, it's 1 instead). For example, a 57x43 image would have mipmaps like:

level 0: 57x43
level 1: 28x21
level 2: 14x10
level 3: 7x5
level 4: 3x2
level 5: 1x1


UV mapping, LOD selection, and filtering work just the same way as for power-of-two texture sizes.

Generating good quality mips for a non-power-of-two texture is a little trickier, as you can't simply average a 2x2 box of pixels to downsample in all cases. However, a 2x2 box filter wasn't that great to begin with, so using a better downsampling filter such as Mitchell-Netravali is recommended regardless of the texture size.