  Several problems at the interface between the field-theoretical description
of the Casimir effect and experiments on measuring the Casimir force are
discussed. One of these problems is connected with the definition of the
Casimir free energy in ideal metal rectangular boxes satisfying the general
physical requirements. It is shown that the consideration of rectangular boxes
with a partition (piston) does not negate the previously known results obtained
for boxes without a piston. Both sets of results are found to be in mutual
agreement. Another problem is related to the use of the proximity force
approximation for the interpretation of the experimental data and to the search
of analytical results beyond the PFA based on the first principles of quantum
field theory. Next, we discuss concepts of experimental precision and of the
measure of agreement between experiment and theory. The fundamental difference
between these two concepts is clarified. Finally, recent approach to the
thermal Casimir force taking screening effects into account is applied to real
metals. It is shown that this approach is thermodynamically and experimentally
inconsistent. The physical reasons of this inconsistency are connected with the
violation of thermal equilibrium which is the basic applicability condition of
the Lifshitz theory.
