  Our recent theoretical developments related to the nonrelativistic and
relativistic fluctuation-electromagnetic interactions of bodies with different
temperatures moving translationally and (or) rotationally relative to each
other are briefly summarized. Three basic geometrical configurations and
physical systems are discussed: "a small particle and a thick plate (i);"a
small particle in radiation vacuum background" (ii), and "two thick plates in
relative motion (iii) -classical Casimir-Lifshitz configuration with allowance
for relative motion and different temperatures of plates. For the third
configuration, it is shown that the theory of friction and heat exchange by
Levin-Polevoi-Rytov proves to be quite adequate contrary to the settled point
of view of many authors.
