  I review results concerning the derivation of effective equations for the
dynamics of interacting Fermi gases in a high-density regime of mean-field
type. Three levels of effective theories, increasing in precision, can be
distinguished: the semiclassical theory given by the Vlasov equation, the
mean-field theory given by the Hartree-Fock equation, and the description of
the dominant effects of non-trivial entanglement by the random phase
approximation. Particular attention is given to the discussion of admissible
initial data, and I present an example of a realistic quantum quench that can
be approximated by Hartree-Fock dynamics.
