The mouse, as a model organism to study the brain, gives us unprecedented experimental access to the mammalian cerebral cortex. By determining the cortex's cellular composition, revealing the interaction between its different components, and systematically perturbing these components, we are obtaining mechanistic insight into some of the most basic properties of cortical function. In this review, we describe recent advances in our understanding of how circuits of cortical neurons implement computations, as revealed by the study of mouse primary visual cortex. Further, we discuss how studying the mouse has broadened our understanding of the range of computations performed by visual cortex. Finally, we address how future approaches will fulfill the promise of the mouse in elucidating fundamental operations of cortex. Expected final online publication date for the Annual Review of Neuroscience, Volume 44 is July 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.