Sleep spindles are burstlike signals in the electroencephalogram (EEG) of the sleeping mammalian brain and electrical surface correlates of neuronal oscillations in thalamus. As one of the most inheritable sleep EEG signatures, sleep spindles probably reflect the strength and malleability of thalamocortical circuits that underlie individual cognitive profiles. We review the characteristics, organization, regulation, and origins of sleep spindles and their implication in non-rapid-eye-movement sleep (NREMS) and its functions, focusing on human and rodent. Spatially, sleep spindle-related neuronal activity appears on scales ranging from small thalamic circuits to functional cortical areas, and generates a cortical state favoring intracortical plasticity while limiting cortical output. Temporally, sleep spindles are discrete events, part of a continuous power band, and elements grouped on an infraslow time scale over which NREMS alternates between continuity and fragility. We synthesize diverse and seemingly unlinked functions of sleep spindles for sleep architecture, sensory processing, synaptic plasticity, memory formation, and cognitive abilities into a unifying sleep spindle concept, according to which sleep spindles 1) generate neural conditions of large-scale functional connectivity and plasticity that outlast their appearance as discrete EEG events, 2) appear preferentially in thalamic circuits engaged in learning and attention-based experience during wakefulness, and 3) enable a selective reactivation and routing of wake-instated neuronal traces between brain areas such as hippocampus and cortex. Their fine spatiotemporal organization reflects NREMS as a physiological state coordinated over brain and body and may indicate, if not anticipate and ultimately differentiate, pathologies in sleep and neurodevelopmental, -degenerative, and -psychiatric conditions.