  We provide an overview of our numerical and analytical studies of isolated
interacting quantum systems that are quenched out of equilibrium
instantaneously. We describe the relaxation process to a new equilibrium and
obtain lower bounds for the relaxation time of full random matrices and
realistic systems with two-body interactions. We show that the size of the time
fluctuations after relaxation decays exponentially with system size for systems
without too many degeneracies. We also discuss the conditions for
thermalization and demonstrate that it can happen after local and global
quenches in space. The analyses are developed for systems, initial states, and
few-body observables accessible to experiments with optical lattices.
