We present recent experimental and theoretical results that link the phenomenon of dielectric relaxation in nematic liquid crystals to their fast electro-optical switching and to the problem of dielectric heating. We develop the theoretical model that allows one to relate director reorientation to the "history" of the electric field. We present an experiment that is well described by the proposed theory but which cannot be described within the classic model of an instantaneous response. We also analyze the effect of dielectric heating that is especially profound at the frequencies corresponding to dielectric relaxation.