  We discuss a recent approach for overcoming the poor convergence of the
perturbative expansion for the thermodynamic potential of QCD. This approach is
based on self-consistent approximations which allow for a gauge-invariant and
manifestly ultraviolet-finite resummation of the essential physics of the hard
thermal/dense loops. The results thus obtained are in good agreement with
available lattice data down to temperatures of about twice the critical
temperature. Calculations for a plasma with finite quark density (i.e., with a
non-zero chemical potential $\mu$) are no more difficult than at $\mu=0$.
