In the mixed state of a type II superconductor quasiparticles and magnetic flux quanta respond to a temperature gradient by thermal diffusion, in this way generating the Seebeck and Nernst effects, respectively. Our understanding of the Seebeck effect originates from an extension of the two-fluid counterflow concept, originally introduced by Ginzburg, to the situation where vortices (with a normal core) are imbedded in the superconducting phase. This mechanism results in an intimate connection between the Seebeck coefficient and the electric resistivity due to vortex motion. In all thermal diffusion processes it is the transport entropy of the diffusing species that determines the driving force, and the physics of this quantity is illustrated. Our discussion of the experimental side concentrates on the recent work performed with the cuprate superconductors. The characteristic broadening of the resistive transition in the mixed state, found in these materials due to their high anisotropy and the peculiar vortex structure (pancake vortices), results in a similar broadening of the temperature regime where the Seebeck and Nernst effects appear. In the cuprate superconductors fluctuation effects are highly pronounced because of the large anisotropy, small coherence length, and high critical temperature of these materials. Here the Nernst effect yields particularly useful information since it nearly vanishes in the normal state, and complicated subtraction procedures are unnecessary. As in all transport phenomena, the Hall angle also appears in the thermal diffusion processes, and a summarizing discussion is given. The observation of an unusually large Hall angle for the thermal diffusion of vortices still remains puzzling. A tentative explanation is based on the thermal generation of unbound vortex-antivortex pairs.