Spatial inhomogeneities, e.g. dislocations or impurities are inevitable features of realistic systems. In condensed matter physics, the dynamics of disorder is usually slow compared to experimental time scales, thus inhomogeneities are well approximated by time-independent, quenched disorder. Although being a microscopic perturbation, quenched disorder may dramatically change the large-scale critical behavior of the system. A paradigmatic example is the zero temperature quantum phase transition of the quantum Ising model, where the system exhibits exotic, infinitely disordered critical behavior. Besides the quantum Ising model, there is a huge number of further interesting examples, such as the random walk in 1D, the 1D Hubbard model, the Mott metal-insulator transition in 2D, localization of a random polymer at an interface, random exclusion processes and trap models, driven lattice gases and reaction diffusion models, as well as a number of classical and quantum spin systems. In the understanding of the phenomena the strong disorder renormalization group (SDRG) method plays a crucial role, yielding exact analytical results in 1D. Unfortunately, in higher dimensional systems the method is only numerically applicable. In 2D this enabled to study only relatively small systems with a limited accuracy. In the experimentally important three dimensional case no quantitative results have been achieved. In this talk I will give an overview about my analytical and numerical results concerning the SDRG method, leading to the first quantitative results in 3 (and higher) dimensions. The obtained results are directly applicable also for the contact process, which is a simple model of infection spreading.