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Decades of findings in psychology suggest that human belief is thoroughly irrational. At best, beliefs might be formed by heuristic processes that predictably lead to suboptimal outcomes. At worst, they are slaves to motivated reasoning, which allows people to come to whichever conclusions they prefer. In this article, we suggest that belief updating, narrowly construed, may be a rational process that is uniquely sensitive to evidence and cognitively impenetrable to desires or incentives. Before any updating can occur, however, a series of processes mediate between information in the world and subjectively compelling evidence. We distinguish between updating proper and processes of evidence search, acceptance, hypothesis specification, integration of relevant information, and reasoning. We review research highlighting the computational difficulty inherent to each of these problems and conclude that solutions must be heuristic and fallible. Beyond incidental failures, evidence evaluation processes-unlike updating-are penetrable to motivation and as such, may be biased by people's desires and goals. In light of this distinction, we propose a theoretical framework for integrating research on belief which divides the cognitive processes involved in belief into two distinct levels. At Level 1, updating is suggested to be approximately Bayesian and impenetrable to desires and goals. In contrast, Level 2 processes, which search for and evaluate evidence, are cognitively penetrable. In addition, we emphasize that Level 2 processes are necessarily heuristic and exhibit bounded rationality (Simon, 1956) given the difficulty of the problems they have to solve. Finally, we specify an additional set of relatively invariant characteristics, which influence how Level 2 processes are employed by making different methods of information processing available. Our framework offers a more nuanced understanding of belief, permits a granular localization of irrationality, and may help reconcile extant debates in the literature. (PsycInfo Database Record (c) 2024 APA, all rights reserved).