This article reviews the mechanisms through which molecules adsorbed to the surfaces of semiconductor nanocrystals, quantum dots (QDs), influence the pathways for and dynamics of intra- and interband exciton relaxation in these nanostructures. In many cases, the surface chemistry of the QDs determines the competition between Auger relaxation and electronic-to-vibrational energy transfer in the intraband cooling of hot carriers, and between electron or hole-trapping processes and radiative recombination in relaxation of band-edge excitons. The latter competition determines the photoluminescence quantum yield of the nanocrystals, which is predictable through a set of mostly phenomenological models that link the surface coverage of ligands with specific chemical properties to the rate constants for nonradiative exciton decay.