The neural output of the cochlea consists of a structured spectral representation of the input waveform. Psychophysical studies of frequency selectivity provide measures of the quality of this spectral representation based on the detection of a spectrally narrow signal in the presence of competing acoustic inputs. Results are often interpreted in terms of the underlying physiological processes. The present paper begins with a summary of the basic principles and data and a review of recent efforts to extend the theoretical framework to account for a wider range of phenomena. It then discusses and evaluates specific assumptions concerning the role of suppression in psychophysical measures of frequency selectivity, an area of research that has received much attention in recent years. The goal is to provide a summary of current answers to basic questions at a time of rapidly expanding knowledge about both the physiology and psychophysics of frequency selectivity.