  The poor convergence of quantum field theory at finite temperature has been
one of the main obstacles in the practical applications of thermal QCD for
decades. Here we briefly review the progress of hard-thermal-loop perturbation
theory (HTLpt) in reorganizing the perturbative expansion in order to improve
the convergence. The quantum mechanical anharmonic oscillator is used as a
simple example to show the breakdown of weak-coupling expansion, and
variational perturbation theory is introduced as an effective resummation
scheme for divergent weak-coupling expansions. We discuss HTLpt thermodynamic
calculations for QED, pure-glue QCD, and QCD with N_f=3 up to three-loop order.
The results suggest that HTLpt provides a systematic framework that can be used
to calculate both static and dynamic quantities for temperatures relevant at
LHC.
