  We review recent developments in the theory of interacting quantum
many-particle systems that are not in equilibrium. We focus mainly on the
nonequilibrium generalizations of the flow equation approach and of dynamical
mean-field theory (DMFT). In the nonequilibrium flow equation approach one
first diagonalizes the Hamiltonian iteratively, performs the time evolution in
this diagonal basis, and then transforms back to the original basis, thereby
avoiding a direct perturbation expansion with errors that grow linearly in
time. In nonequilibrium DMFT, on the other hand, the Hubbard model can be
mapped onto a time-dependent self-consistent single-site problem. We discuss
results from the flow equation approach for nonlinear transport in the Kondo
model, and further applications of this method to the relaxation behavior in
the ferromagnetic Kondo model and the Hubbard model after an interaction
quench. For the interaction quench in the Hubbard model, we have also obtained
numerical DMFT results using quantum Monte Carlo simulations. In agreement with
the flow equation approach they show that for weak coupling the system relaxes
to a "prethermalized" intermediate state instead of rapid thermalization. We
discuss the description of nonthermal steady states with generalized Gibbs
ensembles.
