Anderson localization was first discovered for electrons in disordered solids but later was shown to take place for various types of waves in disordered media. For three-dimensional (3D) disorder, it takes place only in a restricted band of frequencies, separated from the rest of the spectrum by mobility edges, and only when the disorder is strong enough. Our recent results indicate that the vector nature of waves (microwaves, light, elastic waves) used in the experiments on Anderson localization, plays an important role. In particular, the transverse electromagnetic waves cannot be localized by a random 3D arrangement of resonant point-like scatterers (atoms), whereas the elastic waves, which have a longitudinal component as well, can be localized in a way very similar to scalar waves. However, the localization of light can still be made possible by putting the atoms in a strong external magnetic field. We will present a unified view on Anderson localization and compute the localization phase diagrams and the critical parameters (mobility edges and critical exponents) of Anderson localization transitions for elastic waves and light scattered by atoms in a strong magnetic field. Despite the differences between these two systems, they turn out to belong to the same universality class.