Two-phase ow models are used to understand the extraction of oil or gas in porous media or store Carbon Dioxide in empty reservoirs. Mathematically the models consist of a system of nonlinear partial di erential equations. The saturation equation is a nonlinear hyperbolic conservation law if the capillary pressure is neglected while the pressure is modeled using an elliptic equation. Some open problems in the theory will be mentioned. Many physical input variables, e.g. rock permeability, realtive permaebilty are determined by measurement processes and hence are prone to uncertainty. Hence one needs to model uncertainty to be able to compute the e ects. For an ecient code one uses the Multi-level Monte Carlo method. This is a joint work with Vitor Alves Pires at ICMC USP.