Three basic hypotheses regarding the speech-understanding difficulties of the elderly are reviewed: the peripheral, central-auditory, and cognitive hypotheses. Evidence obtained in our laboratory and in others is reviewed regarding the viability of each hypothesis. It is concluded that the strongest support exists for the peripheral hypothesis. Specifically, individual variations in the amount of sensorineural hearing loss among the elderly are most responsible for individual variations in speech-understanding performance. ("Speech understanding" is used throughout this article as a general term for the proportion of a speech signal that is accurately perceived by a listener whether in a discrimination, identification, recognition, or comprehension paradigm.) The focus to date, however, has been placed on monaural speech understanding measured in quiet, noise, or reverberation. It is possible that a more complex picture may yet emerge for other forms of temporally distorted speech or for dichotic measures of speech understanding.