Nonequilibrium dynamics of plasmas often requires a kinetic treatment, in particular, on femtosecond time-scales of present short pulse laser-plasma experiments. The collisionless regime is basically described by the Vlasov-Maxwell theory describing the long-range Coulomb interaction between particles by a self-consistent potential. In the present talk, we review the Vlasov approach in quantum mechanics and introduce a formulation, the multistream model, that is particularly well adopted to numerical quantum plasma simulations [1-3]. Furthermore, the role of the quantum-mechanical exchange interaction will be discussed in the framework of the Hartree-Fock theory. Using these methods, we consider small amplitude plasma waves and Landau damping in a Fermi-degenerate state, nonlinear wavebreaking of large amplitude waves, as well as applications to atomic clusters in strong laser fields. As prominent results, subexponential relaxation of plasma waves is found in certain regimes of a fully Fermi-degenerate quantum plasma and the relaxation of Mie-plasmons due to surface-scattering effects can be calculated quantitatively for small spherical metal clusters.
 A. Schmidt-Bleker, W. Gassen, and H.-J. Kull, EPL 95, 55003 (2011)
 W. Steffen and H.-J. Kull, Phys. Rev. E 93, 033207 (2016)
 A. El-Khawaldeh and H.-J. Kull, Phys. Rev. A 95, 043401 (2017)