Decades of research have demonstrated that sleep benefits memory formation and restores cognitive resources. While the behavioral benefits of sleep are well established, the neurophysiological underpinnings are less clear. In particular, it remains unknown how memories are transferred from short- to long-term storage. While initial theories were largely centered on rapid eye movement (REM) sleep, several contemporary theories converged on the notion that non-REM (NREM) sleep is actively engaged in memory consolidation. NREM sleep is dominated by prominent neuronal oscillations, such as cortical slow waves (<1.25 Hz), thalamo-cortical sleep spindles (12-16 Hz), and hippocampal ripple oscillations (80-200 Hz). Here we provide an overview of how selective synchronization of neuronal oscillations promotes information reactivation, transfer and consolidation during sleep. We explore the neocortical-hippocampal dialogue in support of information selection and distribution and we discuss the concept of cross-frequency coupling as a neural mechanism of information transfer. In particular, we focus on how time-varying, oscillatory activity can promote a neurophysiological milieu that mediates neuroplasticity. Taken together, we will review evidence of how sleep provides optimal conditions for neuroplasticity and outline that a disruption of sleep can contribute to age- and disease-related memory impairments and cognitive decline.