Abstract All forms of cognition, whether natural or artificial, are subject to constraints of their computing architecture. This assumption forms the tenet of virtually all general theories of cognition, including those deriving from bounded optimality and bounded rationality. In this letter, we highlight an unresolved puzzle related to this premise: what are these constraints, and why are cognitive architectures subject to cognitive constraints in the first place? First, we lay out some pieces along the puzzle edge, such as computational tradeoffs inherent to neural architectures that give rise to rational bounds of cognition. We then outline critical next steps for characterizing cognitive bounds, proposing that some of these bounds can be subject to modification by cognition and, as such, are part of what is being optimized when cognitive agents decide how to allocate cognitive resources. We conclude that these emerging views may contribute to a more holistic perspective on the nature of cognitive bounds, as well as their alteration subject to cognition.