  Naively resummed perturbative approximations to the thermodynamic functions
of QCD do not converge at phenomenologically relevant temperatures. Here we
review recent results of a three-loop hard-thermal-loop perturbation theory
calculation of the thermodynamic functions of a quark-gluon plasma for general
N_c and N_f. We show comparisons of our recent results with lattice data from
both the hotQCD and Wuppertal-Budapest groups. We demonstrate that the
three-loop hard-thermal-loop perturbation result for QCD thermodynamics agrees
with lattice data down to temperatures T ~ 2 T_c.
