UV
uvs are just gradient on the X and Y axis, and those uvs can be manipulated to do various things.
Radial
Radial UVs can be very useful, they will allow you to map your texture in a radial way and you will be able to add radial or sunken animation.You can simply animate your UVs on the X or Y axis
Here i am using the Radial mapping to drive a uv distortion texture and i use my Y axis to control my color for example
Depth
Depth fade is often used to fade particle at the intersection with the opaque world in order to avoid having some hard edge but since it give us a gradient, we can use it as UVs
It can also be used as a mask