A leading theory for why we sleep focuses on memory consolidation - the process of stabilizing and strengthening newly acquired memories into long-term storage. Consolidation of memory for cognitive strategies and problem-solving skills is enhanced as compared to a period of daytime wakefulness. Importantly, sleep preferentially enhances memory for the cognitive strategy per se, over-and-above the motor skills that are used to execute the strategy. Although it has been known for some time that sleep benefits this type of memory, it is not known how this process unfolds during sleep, or how sleep transforms this memory trace in the brain. Sleep is classified into rapid eye movement (REM) sleep and non-REM (NREM) sleep. The role of REM sleep for consolidation of memory for problem-solving skills remains controversial. In addition, little attention has been paid to the possible distinct roles of phasic REM sleep (i.e., when bursts of eye movements occur) and tonic REM sleep (i.e., the presence of isolated eye movements and the absence of eye movement bursts). REM sleep might favour procedural memory consolidation for cognitive strategies and problem-solving skills, and the specific role of REM sleep in this process might be discernible only by differentiating between phasic and tonic REM states. In addition, fMRI studies have revealed that sleep-related consolidation of the memory trace for simple motor procedural skills is associated with strengthened activity of, and functional connectivity between, key memory-related brain areas (i.e., hippocampal, striatal, and neocortex). However, fMRI techniques have not yet been employed to investigate sleep-related consolidation of procedural memory for cognitive strategies and problem-solving skills. Participants (n=60) performed a procedural memory task involving a cognitive strategy while undergoing functional magnetic resonance imaging (fMRI) before and after a condition of Sleep, Nap, or Wake. Those in the Sleep and Nap condition underwent polysomnography (PSG) to further study the learning-related changes in sleep macrostructure and microstructure. This thesis not only shows that a period of sleep or a nap afford a greater benefit to memory consolidation of a procedural strategy than a period of wake, but more specifically: In Study 1, during sleep, phasic REM sleep theta power was directly associated with overnight improvement on the task, whereas tonic REM sleep sensorimotor rhythm power was greater following a night of learning compared to a non-learning control night. In Study 2, we show that distinct hippocampal, striatal, and cortical areas associated with strategy learning are preferentially enhanced. Study 3 reveals that the functional communication among these brain areas is greater following sleep compared to a daytime nap or day of wakefulness. Sleep-related changes in brain activation and functional connectivity were both correlated with improved performance from before to after a period of sleep. Overall, findings from this thesis support the benefit of sleep at the behavioural and systems level for consolidating procedural memory involving cognitive strategies used to solve problems. The findings suggest that the multifaceted nature of REM sleep must be examined separately by its phasic and tonic states, to identify the active role of REM sleep for consolidating memory. Further, the consolidation of the memory trace is reflected through activation of, and communication between hippocampal, striatal, and neocortical brain areas. In summary, this thesis shows that sleep actively consolidates memory for cognitive strategies and problem-solving skills.