Given an action of the 1-dimensional complex torus on a normal projective variety, one gets a set of birationally equivalent GIT quotients. In this talk we will consider the opposite question: given a birational map, we want to realize it as the induced birational map between two GIT quotients of a projective variety by a torus action. We will present examples of this two-way correspondence and discuss its combinatorial counterpart, appearing in the context of toric varieties.