Affective experiences are commonly represented by either transient emotional reactions to discrete events or longer term, sustained mood states that are characterized by a more diffuse and global nature. While both have considerable influence in shaping memory, their interaction can produce mood-congruent memory (MCM), a psychological phenomenon where emotional memory is biased toward content affectively congruent with a past or current mood. The study of MCM has direct implications for understanding how memory biases form in daily life, as well as debilitating negative memory schemas that contribute to mood disorders such as depression. To elucidate the factors that influence the presence and strength of MCM, here we systematically review the literature for studies that assessed MCM by inducing mood in healthy participants. We observe that MCM is often reported as enhanced accuracy for previously encoded mood-congruent content or preferential recall for mood-congruent autobiographical events, but may also manifest as false memory for mood-congruent lures. We discuss the relevant conditions that shape these effects, as well as instances of mood-incongruent recall that facilitate mood repair. Further, we provide guiding methodological and theoretical considerations, emphasizing the limited neuroimaging research in this area and the need for a renewed focus on memory consolidation. Accordingly, we propose a theoretical framework for studying the neural basis of MCM based on the neurobiological underpinnings of mood and emotion. In doing so, we review evidence for associative network models of spreading activation, while also considering alternative models informed by the cognitive neuroscience literature of emotional memory bias.