Abstract
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.
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