The acceptance of cochlear implantation as an effective and safe treatment for deafness has increased steadily over the past quarter century. The earliest devices were the first implanted prostheses found to be successful in compensating partially for lost sensory function by direct electrical stimulation of nerves. Initially, the main intention was to provide limited auditory sensations to people with profound or total sensorineural hearing impairment in both ears. Although the first cochlear implants aimed to provide patients with little more than awareness of environmental sounds and some cues to assist visual speech-reading, the technology has advanced rapidly. Currently, most people with modern cochlear implant systems can understand speech using the device alone, at least in favorable listening conditions. In recent years, an increasing research effort has been directed towards implant users’ perception of nonspeech sounds, especially music. This paper reviews that research, discusses the published experimental results in terms of both psychophysical observations and device function, and concludes with some practical suggestions about how perception of music might be enhanced for implant recipients in the future. The most significant findings of past research are: (1) On average, implant users perceive rhythm about as well as listeners with normal hearing; (2) Even with technically sophisticated multiple-channel sound processors, recognition of melodies, especially without rhythmic or verbal cues, is poor, with performance at little better than chance levels for many implant users; (3) Perception of timbre, which is usually evaluated by experimental procedures that require subjects to identify musical instrument sounds, is generally unsatisfactory; (4) Implant users tend to rate the quality of musical sounds as less pleasant than listeners with normal hearing; (5) Auditory training programs that have been devised specifically to provide implant users with structured musical listening experience may improve the subjective acceptability of music that is heard through a prosthesis; (6) Pitch perception might be improved by designing innovative sound processors that use both temporal and spatial patterns of electric stimulation more effectively and precisely to overcome the inherent limitations of signal coding in existing implant systems; (7) For the growing population of implant recipients who have usable acoustic hearing, at least for low-frequency sounds, perception of music is likely to be much better with combined acoustic and electric stimulation than is typical for deaf people who rely solely on the hearing provided by their prostheses.