A fundamental problem from biology is finding conditions under which interacting species coexist or go extinct. I present results that lay the foundation for a general theory of stochastic coexistence. This theory extends and makes rigorous Modern Coexistence Theory and leads to resolving a number of conjectures due to Chesson, Ellner, and Palis. I explain how this theory can be used to complete the classification of three-species stochastic ecological systems and end with an important example that shows that random environmental fluctuations can rescue species from extinction.