In ordinary listening environments, acoustic signals reaching the ears directly from real sound sources are followed after a few milliseconds by early reflections arriving from nearby surfaces. Early reflections are spectrotemporally similar to their source signals but commonly carry spatial acoustic cues unrelated to the source location. Humans and many other animals, including nonmammalian and even invertebrate animals, are nonetheless able to effectively localize sound sources in such environments, even in the absence of disambiguating visual cues. Robust source localization despite concurrent or nearly concurrent spurious spatial acoustic information is commonly attributed to an assortment of perceptual phenomena collectively termed "the precedence effect," characterizing the perceptual dominance of spatial information carried by the first-arriving signal. Here, we highlight recent progress and changes in the understanding of the precedence effect and related phenomena.