Cognitive neuroscience has highlighted the cerebral cortex while often overlooking subcortical structures. This cortical proclivity is found in basic and translational research on many aspects of cognition, especially higher cognitive domains such as language, reading, music, and math. We suggest that, for both anatomical and evolutionary reasons, multiple subcortical structures play substantial roles across higher and lower cognition. We present a comprehensive review of existing evidence, which indeed reveals extensive subcortical contributions in multiple cognitive domains. We argue that the findings are overall both real and important. Next, we advance a theoretical framework to capture the nature of (sub)cortical contributions to cognition. Finally, we propose how new subcortical cognitive roles can be identified by leveraging anatomical and evolutionary principles, and we describe specific methods that can be used to reveal subcortical cognition. Altogether, this review aims to advance cognitive neuroscience by highlighting subcortical cognition and facilitating its future investigation.