The rapid point-to-point movements of the eyes called saccades are the most commonly made movement by humans, yet differ from nearly every other type of motor output in that they are completed too quickly to be adjusted during their execution by visual feedback. Saccadic accuracy remains quite high over a lifetime despite inevitable changes to the physical structures controlling the eyes, indicating that the oculomotor system actively monitors and adjusts motor commands to achieve consistent behavioral production. Indeed, it seems that beyond the ability to compensate for slow, age-related bodily changes, saccades can be modified following traumatic injury or pathology that affects their production, or in response to more short-term systematic alterations to post-saccadic visual feedback in a laboratory setting. These forms of plasticity rely on the visual detection of accuracy errors by a unified set of mechanisms that support the process known as saccade adaptation. Saccade adaptation has been mostly studied as a phenomenon in its own right, outside of motor learning in general. Here, we highlight the commonalities between eye and arm movement adaptation by reviewing the literature across these fields wherever there are compelling overlapping theories or data. Recent exciting findings are challenging previous interpretations of the underlying mechanisms of saccade adaptation with the incorporation of concepts including prediction, reinforcement and contextual learning. We review the emerging ideas and evidence with particular emphasis on the important contributions made by Josh Wallman in this sphere over the past 15 years.