This paper exposes some topics and questions about music improvisation using computers that the author has considered during more than a decade of experience as a performer, composer, software designer and educator. After a quick review of several of his previous interactive music systems, some of those issues are then confronted in FMOL, a program initially designed as a tool for on-line collaborative composition that has been used by hundreds of on-line composers, and which is also being employed by the author in free-form audiovisual improvisation concerts.