We describe multiphase flow problems and in more details, one of the models, used to simulate such phenomena, the so-called diffuse interface methods. One of the main modelling tool for these methods in the Cahn-Hilliard equation. The corresponding discrete systems to be solved are also of two-by-two block form and some special preconditioners for those are included in the presentation. In presence of convection, the Cahn-Hilliard is coupled to the variable density Navier-Stokes equation. We finalize the presentation with some details on that coupled system and show some results on simulating the so-called Rayleigh-Taylor instability.