  We review recent theoretical advances in cold atom physics concentrating on
strongly correlated cold atoms in optical lattices. We discuss recently
developed quantum optical tools for manipulating atoms and show how they can be
used to realize a wide range of many body Hamiltonians. Then we describe
connections and differences to condensed matter physics and present
applications in the fields of quantum computing and quantum simulations.
Finally we explain how defects and atomic quantum dots can be introduced in a
controlled way in optical lattice systems.
