  Our aim is to give a self-contained review of recent advances in the analytic
description of the deconfinement transition and determination of the
deconfinement temperature in lattice QCD at large N. We also include some new
results, as for instance in the comparison of the analytic results with
Montecarlo simulations. We first review the general set-up of finite
temperature lattice gauge theories, using asymmetric lattices, and develop a
consistent perturbative expansion in the coupling $\beta_s$ of the space-like
plaquettes. We study in detail the effective models for the Polyakov loop
obtained, in the zeroth order approximation in $\beta_s$, both from the Wilson
action (symmetric lattice) and from the heat kernel action (completely
asymmetric lattice). The distinctive feature of the heat kernel model is its
relation with two-dimensional QCD on a cylinder; the Wilson model, on the other
hand, can be exactly reduced to a twisted one-plaquette model via a procedure
of the Eguchi-Kawai type. In the weak coupling regime both models can be
related to exactly solvable Kazakov-Migdal matrix models. The instability of
the weak coupling solution is due in both cases to a condensation of
instantons; in the heat kernel case, it is directly related to the
Douglas-Kazakov transition of QCD2. A detailed analysis of these results
provides rather accurate predictions of the deconfinement temperature. In spite
of the zeroth order approximation they are in good agreement with the
Montecarlo simulations in 2+1 dimensions, while in 3+1 dimensions they only
agree with the Montecarlo results away from the continuum limit.
