The properties of hot electrons in systems where electrons and phonons experience quantum confinement are reviewed. The modifications to the behaviour of electrons and phonons brought about by confinement are described, particularly with reference to the principal scattering mechanisms. The latter include the interaction with longitudinal optical phonons and plasmons, along with carrier-carrier effects. Some conflict in the literature concerning Fuchs-Kliewer polaritons is discussed. Low-temperature interactions with acoustic phonons are described. A central topic is that of energy relaxation, and the experimental and theoretical data relating to this form a large part of the review. Energy relaxation mechanisms in the femtosecond to nanosecond regimes, including intersubband and well-capture processes, are eventually summarized. An equally large section deals with hot-electron transport; in which negative differential resistance and other instabilities associated with parallel transport are discussed before turning to ballistic transport and impact ionization.