We describe a novel approach for up-scaling of geological models of heterogeneous reservoirs. The method, which is based on the use of wavelet transformations, incorporates all the relevant data on the permeability, porosity, and other important properties of a reservoir at all the important scales. It generates a nonuniform computational grid which preserves its resolved structure in the regions around the wells and in the high-permeability zones, but is scaled up in the rest of the geological model. To demonstrate the accuracy and efficiency of the method, we apply it to the study of three important problems, namely, the pressure transient analysis, unstable miscible displacements, and two-phase flows. In the study of multiphase flows, we apply a new and robust front detection method. The numerical dispersion is eliminated by a highorder total variation diminishing (TVD) method which yields results that are as accurate as those obtained by the dual-mesh methods, but with a greatly-reduced computational cost. The speed-up in the computations is up to three orders of magnitude.