Neuroimaging has revealed robust interactions between the prefrontal cortex and the hippocampus when people stop memory retrieval. Efforts to stop retrieval can arise when people encounter reminders to unpleasant thoughts they prefer not to think about. Retrieval stopping suppresses hippocampal and amygdala activity, especially when cues elicit aversive memory intrusions, via a broad inhibitory control capacity enabling prepotent response suppression. Repeated retrieval stopping reduces intrusions of unpleasant memories and diminishes their affective tone, outcomes resembling those achieved by the extinction of conditioned emotional responses. Despite this resemblance, the role of inhibitory fronto-hippocampal interactions and retrieval stopping broadly in extinction has received little attention. Here we integrate human and animal research on extinction and retrieval stopping. We argue that reconceptualising extinction to integrate mnemonic inhibitory control with learning would yield a greater understanding of extinction's relevance to mental health. We hypothesize that fear extinction spontaneously engages retrieval stopping across species, and that controlled suppression of hippocampal and amygdala activity by the prefrontal cortex reduces fearful thoughts. Moreover, we argue that retrieval stopping recruits extinction circuitry to achieve affect regulation, linking extinction to how humans cope with intrusive thoughts. We discuss novel hypotheses derived from this theoretical synthesis.