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In this essay I explore the creation of interactive, improvising computer partners. I consider different forms of interaction with computer musical collaborators, be it through traditional musical instruments or alternative controllers. I discuss the work of David Cope, particularly his musical analysis and composition program ​Experiments in Musical Intelligence​, George E. Lewis and his musical improviser ​Voyager​, and finally Eduardo Reck Miranda’s work in algorithmic composition and alternative controllers. The ideas of each of these artists have significant implications for the design of interactive music systems and form the basis of my model of computer improvisation. My approach to improvisation is informed by various styles of the Western tradition—primarily jazz—from very open improvisation (free jazz) to highly structured improvisation.I begin by analysing key ideas behind interactive music systems, such as creating dialogue and reactivity compared to compliance. I then discuss how Cope’s EMI can be utilised as a framework for analysis and improvisation, and discuss other ways of listening and understanding incoming music. This is followed by a comparison of some forms of interaction and algorithmic composition, which comprises the main component of musical generation used by these computer systems. I conclude by discussing my own implementations of these concepts in the piece ​Henonistic​.