Descriptive set theory is the area of mathematics concerned with developing the theory of definable sets in Polish spaces (e.g., sets of reals). In recent years there has been much attention focused on developing the theory of more general classes of definable objects. Since a natural class of examples comes from taking the quotient of a Polish space by a definable equivalence relation, this study involves interaction between descriptive set theory, dynamics, and even geometric group theory. Also involved in the program are strong set theoretic regularity axioms such as the axiom of determinacy.