This talk will focus on orthogonal polynomials whose corresponding measure of orthogonality is not supported on the real line or unit circle. In this setting, the orthonormal polynomials do not satisfy a three-term recurrence relation. However, many theorems from the classical settings of the real line and unit circle can be reformulated to apply to this more general situation. The first part of this talk will present some history and motivation for studying these polynomials and we will conclude by presenting some new results.