He is featured leading his own groups as a sideman or collaborator on more than 170 recordings on the labels ECM, ESPdisk, Clean Feed, Hat Hut, Aum Fidelity, Avant, OkkaDisk, Not Two, Soul Note, Leo, No Business, Rogue Art, Relative Pitch, Incus, RareNoise, Fundacja Sluchaj, Mahakala Music, his own labels Riti and Glacial Erratic and others. Morris has toured extensively throughout North America and Europe as well as in Brazil, Korea and Japan. He has lectured and conducted workshops on his own music and on improvisation throughout the U.S, including at Princeton University, Dartmouth College and Harvard University as well as in Canada, Korea, Netherlands, Portugal, Sweden, Belgium and Ireland.. Since 2000, he has been on the faculty in the Jazz and Contemporary Musical Arts Department at New England Conservatory of Music. Morris is the author of the book, Perpetual Frontier: The Properties of Free Music (Riti Publishing 2012).