This paper is concerned with the craft and pedagogy of contemporary classical composition, starting with an examination of French pedagogy as I received it from Darius Milhaud and Nadia Boulanger in the late 1950s. I discuss their different points of view (briefly the global approach to composition vs. what might be termed the molecular), the composition process itself (what can and what cannot be taught), counterpoint, improvisation, writer's block, the current state of the art, our sister arts, and the changing audience for serious music, along with the increasing importance of improvisation and world music in composition and its pedagogy. I also discuss how many of these elements were implemented in the model Comprehensive Musicianship curriculum at San Diego State University that I designed and directed from 1967 until 2003.