  We review recent results on many-body localization for two explicitly
analyzable models of many-body quantum systems, the XY spin chain in
transversal magnetic field as well as interacting systems of harmonic quantum
oscillators. In both models the presence of disorder leads to dynamical
localization in the form of zero-velocity Lieb-Robinson bounds and to
exponential decay of ground state correlations. Moreover, for oscillator
systems one can also show exponential decay of thermal states as well as an
area law bound for the entanglement entropy of ground and thermal states. The
key fact which allows a rigorous analysis of these models is that they are
given by many-body Hamiltonians which can be reduced to effective single
particle Hamiltonians.
