Completely positive linear mappings between C*-algebras were originally developed in the 1950's as a special case of positive linear operators between matrix algebras. Within the last two decades, mathematical physicists have determined that completely positive maps play a crucial role in quantum information theory as structures which model information transfer between quantum systems. This talk will serve as an introduction to two classes of completely positive maps: the Schur maps which arise from the Schur matrix product and maps which are equal to their adjoint. After focusing on results concerning the geometry of these two sets of CP maps, we introduce a general framework that unifies certain classes of CP maps in terms of C*-subalgebras of Mn.