We've known since childhood that symmetry can be a very powerful tool in solving partial differential equations. With a little symmetry, one can reduce the number of independent variables, whereas with some more symmetry one can usually separate variables and reduce the problem to solving ordinary differential equations. Given enough symmetry, though, partial differential equations become algebraic. A large body of current research in our field requires finding solutions to the (super)gravity field equations and in this talk I will motivate the search for homogeneous supergravity backgrounds and mention some recent results in this area.