Some diffuse interface models of two-phase flow are discussed.  Mixed FEM and FD schemes are used 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.  Both numerical implementation issues and convergence analyses are focused. Finally some extensions of the schemes to approximate solutions for diffuse interface flow models with large differences in density will be discussed.