Meaningful visual experience requires computations that identify objects as the same persisting individuals over time, motion, and through periods of occlusion. Without such representations the visual world would appear unconnected from moment to moment. The experiments presented here marshal a variety of evidence to uncover the resources and heuristics employed by our visual systems to produce representations of objects that persist. In addition, these studies explore the ways that persisting object representations go on to form a crucial building block over which further processing takes place. Specifically, a series of behavioral experiments with humans characterizes the role of persisting objects in constraining working memory and in guiding the distribution of visual attention, and a behavioral experiment with nonhuman primates reveals how these representations can affect real world behaviors. Overall, this research suggests that the basic challenges met by the visual system can have far-reaching consequences for cognition, affecting how an organism attends to the world, what it remembers, and even how it behaves.