  The properties of quantum-chromo dynamics (QCD) nowadays are accessable by
lattice QCD calculations at vanishing quark chemical potential $\mu_q$=0 but
often lack a transparent physical interpretation. In this review we report
about results from an extended dynamical quasiparticle model (DQPM$^*$) in
which the effective parton propagators have a complex selfenergy that depends
on the temperature $T$ of the medium as well as on the chemical potential
$\mu_q$ and the parton three-momentum ${\boldsymbol p}$ with respect to the
medium at rest. It is demonstrated that this approach allows for a good
description of QCD thermodynamics with respect to the entropy density, pressure
etc. above the critical temperature $T_c \approx$ 158 MeV. Furthermore, the
quark susceptibility $\chi_q$ and the quark number density $n_q$ are found to
be reproduced simultaneously at zero and finite quark chemical potential. The
shear and bulk viscosities $\eta, \zeta$, and the electric conductivity
$\sigma_e$ from the DQPM$^*$ also turn out in close agreement with lattice
results for $\mu_q$ =0. The DQPM$^*$, furthermore, allows to evaluate the
momentum $p$, $T$ and $\mu_q$ dependencies of the partonic degrees of freedom
also for larger $\mu_q$ which are mandatory for transport studies of heavy-ion
collisions in the regime 5 GeV $< \sqrt{s_{NN}} <$ 10 GeV. We finally calculate
the charm quark diffusion coefficient $D_s$ -- evaluated from the differential
cross sections of partons in the medium for light and heavy quarks by employing
the propagators and couplings from the DQPM -- and compare to the available
lattice data. It is argued that the complete set of observables allows for a
transparent interpretation of the properties of hot QCD.
