Suppose V is a finite dimensional complex vector space and G is a finite group acting faithfully on V. Then G also acts on the polynomial ring C[V]. Denote by S the subring of C[V] invariant under the action of G. In this talk, we will explore the connection between prime ideals in C[V] and prime ideals in S. In particular, we will attempt to apply the developed theory about prime ideals to the case where G is a finite complex reflection group and P is a height one prime ideal in C[V]. Under these assumptions, we will arrive at somewhat surprising connections to the hyperplane arrangement of G.