Many problems in geometric combinatorics which were originally studied in Euclidean space have interesting analogues in vector spaces over finite fields. One of the most well studied problems in the finite field context is the Erdos-Falconer problem, which asks how large a set must be in order to ensure it determines a positive proportion of all “distances”. One can also ask how large a set must be to determine a positive proportion of congruence classes of point configurations – this can be viewed as a generalization of the first problem, since a distance can be thought of as a congruence class of a two point configuration. We discuss results on these problems.