  In this review we give an overview of recent work on quantum kinetic theories
of plasmas. We focus, in particular, on the case where the electrons are fully
degenerate. For such systems, perturbation methods using the distribution
function can be problematic. Instead we present a model that considers the
dynamics of the Fermi surface. The advantage of this model is that, even though
the value of the distribution function can be greatly perturbed outside the
equilibrium Fermi surface, deformation of Fermi surface is small up very large
amplitudes. Next, we investigate the short-scale dynamics for which the
Wigner-Moyal equation replaces the Vlasov equation. In particular, we study
wave-particle interaction, and deduce that new types of wave damping can occur
due to the simultaneous absorption (or emission) of multiple wave quanta.
Finally, we consider exchange effects within a quantum kinetic formalism to
find a model more accurate than ones using exchange potentials from density
functional theory. We deduce the exchange corrections to the dispersion
relations for Langmuir and ion-acoustic waves. Comparing with results based on
exchange potentials deduced from density functional theory we find that the
latter models are reasonably accurate for Langmuir waves, but rather inaccurate
for ion acoustic waves.
