  We study the electrostatic Casimir effect and related phenomena in
equilibrium statistical mechanics of classical (non-quantum) charged fluids.
The prototype model consists of two identical dielectric slabs in empty space
(the pure Casimir effect) or in the presence of an electrolyte between the
slabs. In the latter case, it is generally believed that the long-ranged
Casimir force due to thermal fluctuations in the slabs is screened by the
electrolyte into some residual short-ranged force. The screening mechanism is
based on a "separation hypothesis": thermal fluctuations of the electrostatic
field in the slabs can be treated separately from the pure image effects of the
"inert" slabs on the electrolyte particles. In this paper, by using a
phenomenological approach under certain conditions, the separation hypothesis
is shown to be valid. The phenomenology is tested on a microscopic model in
which the conducting slabs and the electrolyte are modelled by the symmetric
Coulomb gases of point-like charges with different particle fugacities. The
model is solved in the high-temperature Debye-H\"uckel limit (in two and three
dimensions) and at the free fermion point of the Thirring representation of the
two-dimensional Coulomb gas. The Debye-H\"uckel theory of a Coulomb gas between
dielectric walls is also solved.
