Sensory signals are highly structured in both space and time. These structural regularities in visual information allow expectations to form about future stimulation, thereby facilitating decisions about visual features and objects. Here, we discuss how expectation modulates neural signals and behaviour in humans and other primates. We consider how expectations bias visual activity before a stimulus occurs, and how neural signals elicited by expected and unexpected stimuli differ. We discuss how expectations may influence decision signals at the computational level. Finally, we consider the relationship between visual expectation and related concepts, such as attention and adaptation.