The kinetic equation describing the energy of photons interacting via radiative processes with the surrounding matter is the radiative transfer equation. In this talk, an overview about some recent results in the mathematical analysis of this equation will be presented. In particular, we will consider some developments related to the heat transfer problem concerning the temperature distribution in a body where the heat is transferred by radiation and sometimes by conduction. After an introduction of the kinetic model and a discussion of its physical justification, we show some mathematical properties and some useful analytical tools, which we will apply in the study of radiative heat transfer problems related to well-posedness, diffusion approximation and free-boundary problems. The results that we will present have been obtained in collaboration with A. Felisi, A. Rüland, J.W. Jang and J. J. L. Velázquez.