Modern asset pricing models combine recursive preferences with complex dynamics for the underlying consumption process. The existence of solutions is for many of these models an unsettled question. This paper introduces a novel technique to prove existence and nonexistence, as well as uniqueness for models with recursive preferences. The approach applies to many models of interest, including 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.