Despite extensive evidence on the roles of nonrapid eye movement (NREM) and REM sleep in memory processing, a comprehensive model that integrates their complementary functions remains elusive due to a lack of mechanistic understanding of REM's role in offline memory processing. We present the REM Refining and Rescuing (RnR) Hypothesis, which posits that the principal function of REM sleep is to increase the signal-to-noise ratio within and across memory representations. As such, REM sleep selectively enhances essential nodes within a memory representation while inhibiting the majority (Refine). Additionally, REM sleep modulates weak and strong memory representations so they fall within a similar range of recallability (Rescue). Across multiple NREM-REM cycles, tuning functions of individual memory traces get sharpened, allowing for integration of shared features across representations. We hypothesize that REM sleep's unique cellular, neuromodulatory, and electrophysiological milieu, marked by greater inhibition and a mixed autonomic state of both sympathetic and parasympathetic activity, underpins these processes. The RnR Hypothesis offers a unified framework that explains diverse behavioral and neural outcomes associated with REM sleep, paving the way for future research and a more comprehensive model of sleep-dependent cognitive functions.