Abstract : Complexity of the geometry, randomness of the potential, and many other irregularities of the system can cause powerful, albeit quite different, manifestations of localization, a phenomenon of sudden confinement of waves, or eigenfunctions, to a small portion of the original domain. In the present talk we show that behind a possibly disordered system there exists a structure, referred to as a landscape function, which can predict the location and shape of the localized eigenfunctions, a pattern of their exponential decay, and deliver accurate bounds for the corresponding eigenvalues. In particular, we establish the "landscape law", the first non-asymptotic estimates from above and below on the integrated density of states of the Schroedinger operator using a counting function for the minima of the localization landscape. The results are deterministic, and rely on a new uncertainty principle. Narrowing down to the context of disordered potentials, we derive the best currently available bounds on the integrated density of states for the Anderson model.