How do you map touch points to world space?

Simple question, but the answer might be slightly less simple: How do you map touch points to world space?

Simple example - say you have a sphere, and you want it to move to wherever your finger touches it on your device screen.

Look into Camera.ScreenToWorldPoint (or one of the similar ones). It allows you to convert screenspace coordinates to worldspace. The only problem is that screenspace is 2d and worldspace is 3d, so you might need to construct ray and cast it on the ground to find out where on the ground your sphere should be or something like that. It depends on what your final goal is.