A wealth of recent studies supports a function of sleep on memory and cognitive processing. At a physiological level, sleep supports memory in a number of ways including neural replay and enhanced plasticity in the context of reduced ongoing input. This paper presents behavioral evidence for sleep’s role in selective remembering and forgetting of declarative memories, in generalization of these memories, and in motor skill consolidation. Recent physiological data reviewed suggests how these behavioral changes might be supported by sleep. Importantly, in reviewing these findings, an integrated view of how distinct sleep stages uniquely contribute to memory processing emerges. This model will be useful in developing future behavioral and physiological studies to test predictions that emerge.