The ability to make sense of the music in our environment involves sophisticated cognitive mechanisms that, for most people, are acquired effortlessly and in early life. A special population of individuals, with a disorder termed congenital amusia, report lifelong difficulties in this regard. Exploring the nature of this developmental disorder provides a window onto the cognitive architecture of typical musical processing, as well as allowing a study of the relationship between processing of music and other domains, such as language. The present article considers findings concerning pitch discrimination, pitch memory, contour processing, experiential aspects of music listening in amusia, and emerging evidence concerning the neurobiology of the disorder. A simplified model of melodic processing is outlined, and possible loci of the cognitive deficit are discussed.