He was Head of the Computer Science Department at Carnegie-Mellon University 1971-1979 and Founding Chairman of the Computer Science Department at Columbia University 1979-1989.

He served as Founding Chair of the Computer Science and Telecommunications Board (CSTB) of the National Academies 1986-1992. He served again as chair 2005-2009. He has been appointed as a member of the Division Committee on Engineering and Physical Sciences (DEPS) of the National Academies.

Traub is author or editor of ten books and some one hundred twenty journal articles. He is Editor-in-Chief of the Journal of Complexity and Associate Editor of Complexity.

His numerous honors include election to the National Academy of Engineering in 1985, the 1991 Emanuel R. Piore Gold Medal from IEEE, and the 1992 Distinguished Service Award, Computer Research Association. He is a Fellow of the American Association for the Advancement of Science, the Association for Computing Machinery, and the New York Academy of Sciences. He has been Sherman Fairchild Distinguished Scholar at the California Institute of Technology and received a Distinguished Senior Scientist Award from the Alexander von Humboldt Foundation.  He was selected by the Academia Nazionale dei Lincei in Rome to present the 1993 Lezioni Lincee, a cycle of six lectures. Traub received the 1999 Mayor´s Award for Excellence in Science and Technology. The Award was presented by Mayor Rudy Giuliani at a ceremony in New York City. In May, 2001, he received an honorary Doctorate of Science from the University of Central Florida.

He has served as advisor or consultant to the senior management of numerous organizations including IBM, Hewlett-Packard, Schlumberger, Stanford University, INRIA (Paris), Federal Judiciary Center, DARPA, NSF, and Lucent Technologies. In 2008 he was elected to the Board of Directors of the Marconi Society.