We study the Casimir-Lifshitz interaction out of thermal equilibrium, when the interacting objects are at different temperatures. The analysis is focused on the surface-surface, surface-rarefied body, and surface-atom configurations. A systematic investigation of the contributions to the force coming from the propagating and evanescent components of the electromagnetic radiation is performed. The large distance behaviors of such interactions is discussed, and both analytical and numerical results are compared with the equilibrium ones. A detailed analysis of the crossing between the surface-surface and the surface-rarefied body, and finally the surface-atom force is shown, and a complete derivation and discussion of the recently predicted nonadditivity effects and asymptotic behaviors is presented.