The intense study of interacting galaxies originated in large part with the discovery by IRAS that the most IR-luminous galaxies are nearly all products of collisions and may be the missing link in the chain of evolution from quasars to normal quiescent galaxies (Sanders et al. 1988a,b). These galaxies (with LIR > 1012L⊙) are considered to be the most strongly starbursting of all galaxies in the local universe, have a higher space density than quasars, emit >90% of their power in the IR, are rich in the raw materials of star formation, and to a large extent owe their peculiar morphologies to encounters with other galaxies. The particular importance of IR-luminous galaxies in the grand scheme of cosmology and galaxy evolution has been underscored by the luminosity function studies of Soifer et al. (1986), which indicated that most galaxies have gone through a high-IR luminosity stage. We are using the Hubble Space Telescope to survey the fine-scale features that are associated with the interaction- and activity-related processes that are at work within the Ultraluminous IR Galaxy Sample. It is widely believed that these galaxies are undergoing star formation at a prodigious rate and are abnormally dust-enshrouded. An alternative to the starburst hypothesis is that these galaxies' IR luminosity is powered by a dust-hidden quasar at its center (Sanders et al. 1988a). It is important for our understanding of the evolution of galaxies and quasars to determine which of these two hypotheses is valid, or in which objects they are separately valid.