Simulation of multi-phase flow in porous media has wide applications such as petroleum fields and water resources. In this talk we will introduce physically consistent numerical methods for the simulation of incompressible and immiscible two-phase flow in heterogeneous porous media with capillary pressure. We will also introduce a thermodynamically consistent mathematical model for incompressible and immiscible two-phase flow in porous media with rock compressibility. An energy stable numerical method will be introduced, which can preserve multiple physical properties, including the energy dissipation law, full conservation law for both fluids and pore volumes, and bounds of porosity and saturations. Numerical results will be given to verify the features of the proposed methods.