Most humans report preferring the right hand for a variety of manual actions. Additionally, most humans perform motor tasks better with their right hand, particularly among right-handed individuals, but less so among left-handed people. Some have suggested that asymmetries in performance rather than hand preference may better reflect left hemisphere specializations in motor functions. In contrast to humans, research on performance asymmetries in manual tasks by nonhuman primates has received far less empirical investigation. In this chapter, I review the evidence presented to date on individual- and population-level asymmetries in motor tasks in nonhuman primates. Broadly speaking, studies on motor asymmetries have focused on (1) intermanual differences in grasping morphology and (2) intermanual differences in performance on a variety of different motor tasks. The results suggest that some species show population-level left–right differences in motor skill. Moreover, performance differences between the left and right hands appear to be mediated by preferred hand use but not in a dissociative manner. The collective data suggest that measures of performance asymmetries in different primate species may provide additional insight into theories on the evolution of hemispheric specialization in motor control.