In this talk I will describe some diffuse interface models of two-phase flow.  I will describe in detail mixed finite element and finite difference schemes for a Cahn-Hilliard equation coupled with a non-steady Darcy-Stokes flow that models phase separation and coupled fluid flow in immiscible binary fluids and di-block copolymer melts, to name a couple of applications.  I will focus both on numerical implementation issues for the schemes as well as the convergence analyses. Generally speaking, the time discretization will be based on first or second-order (in time) convex splittings of the energy of the given system of equations. I will show that our schemes are unconditionally energy stable with respect to spatially discrete analogues of the continuous free energy of the system and unconditionally uniquely solvable.  We can show, in addition, that the numerical solutions have other higher-order stabilities.  I will prove that these variables converge with optimal rates in the appropriate energy norms in both two and three dimensions. Finally I will discuss some extensions of the schemes to approximate solutions for diffuse interface flow models with large differences in density.