Stochastic games provide a versatile model for reactive systems that are a'ected by random events. This dissertation advances the algorithmic theory of stochastic games to incorporate multiple players, whose objectives are not necessarily conflicting. The basis of this work is a comprehensive complexitytheoretic analysis of the standard game-theoretic solution concepts in the context of stochastic games over a finite state space. One main result is that the constrained existence of a Nash equilibrium becomes undecidable in this setting. This impossibility result is accompanied by several positive results, including e(cient algorithms for natural special cases.