  For a long time, strong coupling expansions have not been applied
systematically in lattice QCD thermodynamics, in view of the succes of
numerical Monte Carlo studies. The persistent sign problem at finite
baryo-chemical potential, however, has motivated investigations using these
methods, either by themselves or combined with numerical evaluations, as a
route to finite density physics. This article reviews the strategies, by which
a number of qualitative insights have been attained, notably the emergence of
the hadron resonance gas or the identification of the onset transition to
baryon matter in specific regions of the QCD parameter space. For the simpler
case of Yang-Mills theory, the deconfinement transition can be determined
quantitatively even in the scaling region, showing possible prospects for
continuum physics.
