Abstract: Orbit equivalence relations of Polish group actions form a proper subclass of the collection of analytic equivalence relations, and it is a long-standing problem to find a complete characterization of when an arbitrary equivalence relation is induced by some action of a Polish group. Such equivalence relations inherit combinatorial structure from the group actions inducing them, which can be used to analyze their complexity and other properties. In this talk I will discuss work in progress on trying to generalize some of the combinatorics of orbit equivalence relations to general analytic equivalence relations, and how a number of questions about the Borel reducibility hierarchy can be reformulated in this framework.