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Within the framework of unified approach we study the Casimir-Lifshitzinteraction, the van der Waals friction force and the radiative heat transferat nonequilibrium conditions, when the interacting bodies are at differenttemperatures, and they move relative to each other with the arbitrary velocity$V$. The analysis is focused on the surface-surface and surface-particleconfiguration. Our approach is based on the exact solution of electromagneticproblem about the determination of the fluctuating electromagnetic field in thevacuum gap between two flat parallel surfaces moving relative to each otherwith the arbitrary velocity $V$. The velocity dependence of the consideredphenomena is determined by Doppler shift and can be strong for resonant photontunneling between surface modes.  We show that relativistic effects give rise to a mixing of the contributionsfrom the electromagnetic waves with different polarization to the heat transferand the interaction forces. We find that these effects are of the order$(V/c)^2$. The limiting case when one of the bodies is sufficiently rarefiedgives the heat transfer and the interaction forces between a moving smallparticle and a surface.  We also calculate the friction force acting on a particle moving with anarbitrary velocity relative to the black body radiation.

Theory of the interaction forces and the heat transfer between moving bodies mediated by the fluctuating electromagnetic field