  We review recent work on the strong CP problem in the context of realistic
string-inspired models. We discuss the various solutions, review the conjecture
that CP is generally a gauged discrete symmetry in string theory and then
consider models of the Nelson-Barr type. We note that squark non-degeneracy
spoils the Nelson-Barr structure at the one loop level. We stress that string
theory expectations, as well as naturalness arguments, make it very difficult
to avoid the constraints on non-degeneracy.
