At low excitation density, the dynamics of excitons in semiconductor nanocrystals are largely dictated by their interactions with the underlying atomic lattice. This exciton-phonon coupling is responsible, for example, for absorption and luminescence linewidths at elevated temperatures, relaxation processes following optical excitation, and even degradation of quantum coherent applications. Characterizing and understanding exciton-phonon coupling is therefore central to guiding rational design of colloidal nanocrystal materials and their device applications. In this review, we compare different spectroscopic methods of measuring exciton-phonon interactions and the complementary information that they provide. We emphasize the development of a new technique, termed multi-dimensional coherent spectroscopy, that circumvents many of the limitations of traditional methods.