Recent progress on quasi-periodic lattice Schroedinger operators and Hamiltonian PDEs

This is a survey of recent investigations of quasi-periodic localization on lattices (of both methods based on perturbation theory and non-perturbative methods) and of applications of KAM theories in connection with infinite-dimensional Hamiltonian systems. The focus is on applications of these investigations to the Schroedinger equation and the wave equation with periodic boundary conditions, and to non-linear random Schroedinger equations with short-range potentials