  We discuss applications of the theory of Quantum Chaos to one of the paradigm
models of many-body quantum physics -- the Bose-Hubbard model, which describes,
in particular, interacting ultracold Bose atoms in an optical lattice. After
preliminary, pure quantum analysis of the system we introduce the classical
counterpart of the Bose-Hubbard model and the governing semiclassical equations
of motion. We analyze these equations for the problem of Bloch oscillations of
cold atoms where a number of experimental results are available. The review is
written for non-experts and can be viewed as an introduction to the field.
