How do we recognize what one person is saying when others are speaking at the same time? This review summarizes widespread research in psychoacoustics, auditory scene analysis, and attention, all dealing with early processing and selection of speech, which has been stimulated by this question. Important effects occurring at the peripheral and brainstem levels are mutual masking of sounds and “unmasking” resulting from binaural listening. Psychoacoustic models have been developed that can predict these effects accurately, albeit using computational approaches rather than approximations of neural processing. Grouping—the segregation and streaming of sounds—represents a subsequent processing stage that interacts closely with attention. Sounds can be easily grouped—and subsequently selected—using primitive features such as spatial location and fundamental frequency. More complex processing is required when lexical, syntactic, or semantic information is used. Whereas it is now clear that such processing can take place preattentively, there also is evidence that the processing depth depends on the task-relevancy of the sound. This is consistent with the presence of a feedback loop in attentional control, triggering enhancement of to-be-selected input. Despite recent progress, there are still many unresolved issues: there is a need for integrative models that are neurophysiologically plausible, for research into grouping based on other than spatial or voice-related cues, for studies explicitly addressing endogenous and exogenous attention, for an explanation of the remarkable sluggishness of attention focused on dynamically changing sounds, and for research elucidating the distinction between binaural speech perception and sound localization.