  The problem of thermal Casimir force, which consists in disagreement of
theoretical predictions of the fundamental Lifshitz theory with the measurement
data of high precision experiments and some peculiar properties of the Casimir
entropy, is reviewed. We discuss different approaches to the resolution of this
problem proposed in the literature during the last twenty years. Particular
attention is given to the role of the effects of spatial dispersion. The
recently suggested nonlocal Drude-like permittivities which take proper account
of the dissipation of conduction electrons and bring the predictions of the
Lifshitz theory in agreement with experiment and requirements of thermodynamics
are considered. The prospects of this approach in the ultimate resolution of
the problem of thermal Casimir force are evaluated.
