Classical ecological theory relies heavily on the principles of deterministic dynamical systems, and methods from mathematics and physics that are more appropriate for stochastic systems are unfamiliar to many ecologists. As a result, when stochasticity plays an important role in shaping ecological dynamics — as it often does — our ability to fully address certain questions can be limited. In this talk, I will give an overview of some new (or at least newly extended for ecological applications) mathematical methods that bring important new classes of questions into reach.