  I review recent progress in numerical simulations of finite temperature
quantum chromodynamics and discuss the status of some outstanding problems.
Included is (1) a discussion of recent results determining the temperature of
the ``phase transition'' in full QCD, (2) a scaling analysis of the Polyakov
loop variable, leading to the determination of a constituent quark free energy,
(3) studies of critical behavior near the phase transition in two-flavor QCD,
(4) a discussion of problems and new results in thermodynamic simulations with
Wilson fermions, (5) recent results in pure gauge theory with a mixed
fundamental/adjoint action, and (6) the nonperturbative determination of the
equation of state with dynamical fermions included. Finally I mention briefly
new developments in efforts to construct a phenomenology of deconfinement and
chiral symmetry restoration, namely (7) the dual superconducting model and (8)
the instanton model.
