We humans spend almost a third of our lives asleep, andthere is mounting evidence that sleep not only maintains, butactually improves many of our cognitive functions. Mem-ory consolidation–the process of crystallizing and integratingmemories into knowledge and skills–is particularly benefittedby sleep. We survey the evidence that sleep aids memory con-solidation in various declarative and implicit tasks and reviewthe basic neurophysiological structure of sleep with a focus onunderstanding what neural systems are involved. Drawing onmachine learning research, we discuss why it might be usefulfor humans–and robots, perhaps–to have such an offline pe-riod for processing, even though humans are clearly capable oflearning incrementally, online. Finally, we propose and simu-late two mechanisms for use in computational memory modelsto accomplish sleep-based consolidation via either or both 1)re-encoding knowledge representations and 2) reactivating andstrengthening recent memories.