Heat transfers from hot areas to cold ones, in matter or through whatever medium including vacuum. Heat conduction and radiative heat transfer are described by well-established theories at the macroscopic scale, known respectively as Fourier's heat diffusion and incoherent thermal radiation (the latter involves radiation in transparent and semitransparent media). Because the characteristic lengths associated with these two phenomena, such as the mean free path and the wavelength, lie in the micro to nanometre-scale ranges, the theories had to be revisited in these size regimes. The consequence is that the laws describing the heat transfer are different at these scales than at the macroscopic scale. Nanoscale samples or thermal sensors should be analyzed in light of this novel physics.