The simplicity principle, traditionally referred to as Occam's razor, is the idea that simpler explanations of observations should be preferred to more complex ones. In recent decades the principle has been clarified via the incorporation of modern notions of computation and probability, allowing a more precise understanding of how exactly complexity minimization facilitates inference. The simplicity principle has found many applications in modern cognitive science, in contexts as diverse as perception, categorization, reasoning, and neuroscience. In all these areas, the common idea is that the mind seeks the simplest available interpretation of observations— or, more precisely, that it balances a bias toward simplicity with a somewhat opposed constraint to choose models consistent with perceptual or cognitive observations. This brief tutorial surveys some of the uses of the simplicity principle across cognitive science, emphasizing how complexity minimization in a number of forms has been incorporated into probabilistic models of inference. WIREs Cogn Sci 2016, 7:330–340. doi: 10.1002/wcs.1406This article is categorized under: Philosophy > Foundations of Cognitive Science