The intention of most film editing is to create the impression of continuity by editing together discontinuous viewpoints. The continuity editing rules are well established yet there exists an incomplete understanding of their cognitive foundations. This article presents the Attentional Theory of Cinematic Continuity (AToCC), which identifies the critical role visual attention plays in the perception of continuity across cuts and demonstrates how perceptual expectations can be matched across cuts without the need for a coherent representation of the depicted space. The theory explains several key elements of the continuity editing style including match-action, matchedexit/entrances, shot/reverse-shot, the 180° rule, and point-of-view editing. AToCC formalizes insights about viewer cognition that have been latent in the filmmaking community for nearly a century and demonstrates how much vision science in general can learn from film.