In recent years degenerate quantum gases confined in optical lattices developed as a new field of research bridging the areas of quantum optics, atomic physics, and condensed matter physics. It offers the possibility of manipulating quantum many-body systems with an unprecedented flexibility, so that they can be considered as analog simulators of condensed matter systems. Particularly interesting is the possibility of creating strongly correlated bosonic or fermionic systems. We review here recent numerical simulations, where quantum critical behavior is studied both in and out of equilibrium. (c) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.