It is increasingly evident that brain function involves oscillatory activity in various frequency bands. This realization encouraged psychologists to consider that perception and cognition may operate periodically, as a succession of cycles mirroring the underlying oscillatory cycles. This idea, related to the age‐old notion of discrete perception, has resurfaced in recent years, fueled by advances in neuroscientific techniques. Contrary to earlier views of discrete perception as a unitary sampling rhythm affecting all perceptual and cognitive functions, contemporary evidence points not to one but several rhythms of perception that may depend on the sensory modality, the task, the stimulus, the brain region(s) involved, or the state of the subject. In the visual domain for example, a sensory alpha rhythm (∼10 Hz) may coexist with at least one more rhythm performing attentional sampling around 7 Hz. How these multiple periodic functions coordinate with each other and how internal sampling rhythms coordinate with overt sampling behavior are key questions for the future.