  I review recent results on QCD at high temperature on a lattice. Steady
progress with staggered fermions and Wilson type fermions allow a quantitative
description of hot QCD whose accuracy in many cases parallels that of zero
temperature studies. Simulations with chiral quarks are coming of age, and
togheter with theoretical developments trigger interesting developments in the
analysis of the critical region. Issues related with the universality class of
the chiral transition and the fate of the axial symmetry are discussed in the
light of new numerical and analytical results. Transport coefficients and
analysis of bottomonium spectra compare well with results of heavy ion
collisions at RHIC and LHC. Model field theories, lattice simulations and high
temperature systematic expansions help building a coherent picture of the high
temperature phase of QCD. The (strongly coupled) Quark Gluon Plasma is heavily
investigated, and asserts its role as an inspiring theoretical laboratory.
