This research advances our understanding of how experienced composers utilise computers. Understanding is developed through an exploration of computer-assisted composition, informed by an extensive discussion concerning the nature of digital music representations, and exemplified by the actions of five experienced composers. The exploration includes interviews with, and observations of, the composers and an inspection of their tools and processes, the data from which is analysed against a theoretical framework influenced by the fields of compositional theory, creativity, and the philosophy of technology. A new method of considering the broad influences upon composers is described, and includes consideration of the personal, physical, and social contexts in which composers work. The computer-assisted compositional experience is shown to feature an intense involvement in the music making process, which is labelled "compositional engagement." Modes of compositional engagement are presented, which describe a range of computer-assisted compositional approaches. The activities of the case study composers are used to illustrate how the contextual model and compositional engagement theory assist in understanding music composition and the computer. From this analysis it becomes clear how characteristics of the computer music system reflect musical epistemologies and are significant in affecting the compositional process and, to a lesser degree, the compositional outcome, but it is also clear that the composer's ontology and cultural circumstances are of even more significance.