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Motor learning encompasses a wide range of phenomena, ranging from relatively low-level mechanisms for maintaining calibration of our movements, to making high-level cognitive decisions about how to act in a novel situation. We survey the major existing approaches to characterizing motor learning at both the behavioral and neural level. In particular, we critically review two long-standing paradigms used in motor learning research-adaptation and sequence learning. We discuss the extent to which these paradigms can be considered models of motor skill acquisition, defined as the incremental improvement in our ability to rapidly select and then precisely execute appropriate actions, and conclude that they fall short of doing so. We then discuss two classes of emerging research paradigms-learning of arbitrary visuomotor mappings de novo and learning to execute movements with improved acuity-that more effectively address the acquisition of motor skill. Future work will be needed to determine the degree to which laboratory-based studies of skill, as described in this review, will relate to true expertise, which is likely dependent on the effects of practice on multiple cognitive processes that go beyond traditional sensorimotor neural architecture. © 2019 American Physiological Society. Compr Physiol 9:613-663, 2019.