Modern asset pricing models combine recursive preferences with complex dynamics for the underlying consumption process. Existence of solutions is, for many of these models, an unsettled question. This paper introduces a novel technique to prove existence and non-existence as well as uniqueness for models with recursive preferences. The approach applies to many models of interest, such as those with long-run consumption risks, with stochastic volatility and jumps, with time-varying consumption disasters, and with smooth ambiguity aversion and learning. Collectively the proven results settle the existence question for many of today's leading asset pricing models.