Harmonic complex tones are a particularly important class of sounds found in both speech and music. Although these sounds contain multiple frequency components, they are usually perceived as a coherent whole, with a pitch corresponding to the fundamental frequency (F0). However, when two or more harmonic sounds occur concurrently, e.g., at a cocktail party or in a symphony, the auditory system must separate harmonics and assign them to their respective F0s so that a coherent and veridical representation of the different sounds sources is formed. Here we review both psychophysical and neurophysiological (single-unit and evoked-potential) findings, which provide some insight into how, and how well, the auditory system accomplishes this task. A survey of computational models designed to estimate multiple F0s and segregate concurrent sources is followed by a review of the empirical literature on the perception and neural coding of concurrent harmonic sounds, including vowels, as well as findings obtained using single complex tones with mistuned harmonics.