In the first period after the start of finite temperature studies for QCD on the lattice, in 1981, essentially pure SU(2) and SU(3) gauge theory results and a few quenched (i.e., without dynamical quarks) full QCD results were available, all on small lattices. Since then large lattices have come into use for pure SU(2) and SU(3) investigations. On medium size lattices full QCD simulations incorporating dynamical quarks of 0.5 up to 12 flavours and for many differnet quark mass values have been performed. Thsi survey does not cover all of the existing papers on the subject. So we shall omit any details of fermion updates, do not discuss Wilson fermions and other topics, which might be of interest. Also, the attempts made so far to include non-zero chemical potential will not be reviewed, because up to now no realistic (not strong coupling) calculations exist. For more information we suggest to read the conference reviews of fall 1988 by A. Ukawa~1, M.Fukugita~2 and F.Karsch~3. There are some promising new developments since the Lattice 88 and Quark Matter 88 conferences on which we shall report: - the order of the finite temperature transition in models related to the pure SU(3) gauge theory; - first results for full QCD on lattices with large time extend (N_r=8); - the solution of the continuum and lattice perturbation theory discrepancy for the full QCD energy density.
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