Brainstem auditory-evoked potentials (BAEPs) are generated in the ear and brainstem nuclei of the ascending auditory pathways following a transient acoustic stimulus. Because they can be recorded noninvasively in humans, BAEPs have a number of clinical and research applications. This paper reviews the properties of BAEPs, with particular emphasis on those characteristics that are relevant to the acquisition and analysis of the responses. Theories of the neural origins of the responses are reviewed. The dependence of the responses on the stimulus waveform and the problem of stimulus artifact are considered. Then, origins of the background noise are discussed, and the use of linear filtering and methods of artifact detection to improve the signal-to-noise ratio are reviewed. Finally, the problem of identifying parameters to quantify the responses is considered. The definition of response components in terms of response peaks and data on intra- and intersubject variability are reviewed, and the use of algorithms to measure parameters is discussed.