  This review provides a written version of the lectures presented at the
Schladming Winter School 2008, Austria, on 'Nonequilibrium Aspects of Quantum
Field Theory'. In particular, it shows the way from quantum-field theory - in
two-particle irreducible approximation - to the Kadanoff-Baym (KB) equations
and various approximations schemes of the KB equations in phase space. This
ultimately leads to the formulation of an off-shell transport theory that well
incorporates the underlying quantum physics. Remarkably, these transport
equations may be solved within a testparticle representation that allows to
study non-equilibrium quantum systems in the weak and strong coupling regime.
Actual applications to dilepton production in heavy-ion reactions are presented
in comparison with available data. The approach, furthermore, allows to address
the hadronization process from partonic to hadronic degrees of freedom.
