Hand preferences of primates are discussed as part of the broad perspective of brain lateralization in animals, and compared with paw preferences in non-primates. Previously, it has been suggested that primates are more likely to express a species-typical hand preference on complex tasks, especially in the case of coordinated hand use in using tools. I suggest that population-level hand preferences are manifested when the task demands the obligate use of the processing specialization of one hemisphere, and that this depends on the nature of the task rather than its complexity per se. Depending on the species, simple reaching tasks may not demand the obligate use of a specialized hemisphere and so do not constrain limb/hand use. In such cases, individuals may show hand preferences that are associated with consistent differences in behaviour. The individual's hand preference is associated with the expression of behaviour controlled by the hemisphere contralateral to the preferred hand (fear and reactivity in left-handed individuals versus proactivity in right-handed individuals). Recent findings of differences in brain structure between left- and right-handed primates (e.g. somatosensory cortex in marmosets) have been discussed and related to potential evolutionary advances.