Given an action of an algebraic torus T=(k^*)^n on a projective variety X, we can form the Chow or Hilbert quotients. I will describe joint work with Diane Maclagan explaining how knowing equations for X in some projective embedding allows us to compute equations for X//^ch T and X//^H T in many projective embeddings, and to give a GIT description of these spaces. If X degenerates to a toric variety, then we also get degenerations of the Chow and Hilbert quotients to explicitly describable toric varieties.