We consider existence of positive solutions to a Schrodinger system which stems from various aspects in physics, including Bose-Einstein condensates and nonlinear optics. This Schrodinger system has been studied extensively in the literature. Most of the known results are on the system with constant coefficients. Here we study the system with nonconstant coefficients. We present results on existence of ground states, existence of positive solutions at high energy levels, and existence of multiple positive solutions. This is joint work with Haidong Liu.