Categorization is a fundamental cognitive process by which the brain assigns stimuli to behaviorally meaningful groups. Previous studies on visual categorization in primates have identified a hierarchy of cortical areas that are involved in the transformation of veridical sensory information into abstract category representations. However, categorization behaviors are ubiquitous across diverse animal species, even those without a neocortex, motivating the possibility that subcortical regions may contribute to abstract cognition in primates. One candidate structure is the superior colliculus (SC), a midbrain region that is evolutionarily conserved across vertebrates. Although traditionally thought to mediate only reflexive spatial orienting behaviors, especially saccades in primates, the SC is also involved in cognitive tasks that require spatial orienting. In the first part of this thesis, we investigated the involvement of the primate SC in abstract categorization, and show that the SC plays an unexpected key role in higher-order, non-spatial cognition. We trained monkeys to group motion stimuli into categories based on an arbitrary rule, and compared neural activity in the SC and the lateral intraparietal area (LIP), a cortical region previously shown to causally contribute to category decisions, while monkeys performed this task. We observed unexpectedly strong and short-latency category encoding in the SC that was more reliable and arose even earlier than in the LIP. Moreover, monkeys' performance on the categorization task was markedly impaired during reversible inactivation of the SC, indicating that the observed category signals in the SC may causally contribute to category processing. In addition, we show that category and eye movement-related signals are encoded in near-orthogonal subspaces in population activity in the SC, providing an explanation for how a motor structure like the SC can be recruited to participate in more flexible cognitive behaviors. These results extend the well-established role of the SC in spatial orienting to non-spatial, higher-order cognition. In the second part of this thesis, we investigated how behavioral task demands affect category and sensory encoding in the SC, LIP, and the middle temporal area, (MT), an early visual cortical area that is involved in motion processing. We trained monkeys to alternate between blocks of the motion categorization task and blocks in which they passively viewed the same stimuli and received a reward for maintaining fixation. The physical stimulus and stimulus location was identical in the two blocks, but only the categorization task required the monkeys to use the stimulus information to obtain a reward; therefore, we could compare, in the same neurons, how behavioral context affects stimulus encoding. We observed significantly weaker stimulus direction encoding during passive viewing than during the categorization task in all three brain areas. Moreover, although both LIP and SC encoded stimulus category during the categorization task, category encoding was largely absent during passive viewing in both areas. These results indicate that neural populations in LIP and SC can flexibly route sensory input based on current behavioral demands.