Many sound sources emit signals in a predictable manner. The idea that predictability can be exploited to support the segregation of one source's signal emissions from the overlapping signals of other sources has been expressed for a long time. Yet experimental evidence for a strong role of predictability within auditory scene analysis (ASA) has been scarce. Recently, there has been an upsurge in experimental and theoretical work on this topic resulting from fundamental changes in our perspective on how the brain extracts predictability from series of sensory events. Based on effortless predictive processing in the auditory system, it becomes more plausible that predictability would be available as a cue for sound source decomposition. In the present contribution, empirical evidence for such a role of predictability in ASA will be reviewed. It will be shown that predictability affects ASA both when it is present in the sound source of interest (perceptual foreground) and when it is present in other sound sources that the listener wishes to ignore (perceptual background). First evidence pointing toward age-related impairments in the latter capacity will be addressed. Moreover, it will be illustrated how effects of predictability can be shown by means of objective listening tests as well as by subjective report procedures, with the latter approach typically exploiting the multi-stable nature of auditory perception. Critical aspects of study design will be delineated to ensure that predictability effects can be unambiguously interpreted. Possible mechanisms for a functional role of predictability within ASA will be discussed, and an analogy with the old-plus-new heuristic for grouping simultaneous acoustic signals will be suggested.