Improvisation--the act of spontaneously creating music, as opposed to playing music that is strictly pre-composed--is a practice that has most often been taught only in the context of jazz in the classroom. But it has actually been part of many more musical traditions, cultures, and periods. Classical icons like Bach, Mozart, and Beethoven, revered for their composed masterworks, were all expert improvisers, while more recent classical players--pianist Glenn Gould being a particularly striking example--have made a specialty personalizing cadenzas or improvising in the style of a musical era such as the Baroque. This article features several singers and players who are known for their advanced ability as an improviser. It discusses the benefits of teaching improvisation to students and lists books and web sites which provide a wealth of information on teaching improvisation. (Contains 3 resources and 3 online resources.)