This paper reviews the hypothesis of harmonic cancellation according to which an interfering sound is suppressed or canceled on the basis of its harmonicity (or periodicity in the time domain) for the purpose of Auditory Scene Analysis. It defines the concept, discusses theoretical arguments in its favor, and reviews experimental results that support it, or not. If correct, the hypothesis may draw on time-domain processing of temporally accurate neural representations within the brainstem, as required also by the classic equalization-cancellation model of binaural unmasking. The hypothesis predicts that a target sound corrupted by interference will be easier to hear if the interference is harmonic than inharmonic, all else being equal. This prediction is borne out in a number of behavioral studies, but not all. The paper reviews those results, with the aim to understand the inconsistencies and come up with a reliable conclusion for, or against, the hypothesis of harmonic cancellation within the auditory system.