Mundheim practiced at the law firm Shearman & Sterling from 1958, when he was admitted to the New York bar, to 1961. He was Special Counsel to the Securities and Exchange Commission from 1962 to 1963. He was then a visiting professor at Duke Law School in 1964, professor of law at the University of Pennsylvania from 1965 to 1970, visiting professor at Harvard Law School from 1968 to 1969, and Fred Carr Professor of Law and Financial Institutions at the University of Pennsylvania Law School from 1970 to 1980–becoming in 1970 the youngest professor in the law school's history be named an academic chair. Mundheim was General Counsel of the U.S. Treasury Department from 1977 to 1980. He was the Dean of the University of Pennsylvania Law School from 1982 to 1989. He was University Professor of Law and Finance at the University of Pennsylvania from 1980 to 1992. In 1992 Mundheim was Co-Chairman of the law firm Fried, Frank, Harris, Shriver & Jacobson. Mundheim was general counsel of Salomon, Inc. from 1992 to 1997, and of Salomon Smith Barney Holdings from 1997 to 1998. Mundheim was awarded the Officer’s Cross of the Order of Merit of the Federal Republic of Germany in 2007. In 2014, in The Monetary System: Analysis and New Approaches to Regulation, authors Jean-François Serval and Jean-Pascal Tranié noted: "This year, Robert Mundheim was honored by the American Lawyer as a 'Lifetime Achiever', which is one of the most recognized distinctions that an American lawyer can get." He received The New School’s Honorary Degree of Doctor of Humane Letters in 2019. He is now Of Counsel to the law firm Shearman & Sterling, having been with the firm since 1999, and a law professor at the James E. Rogers College of Law at the University of Arizona. The University of Pennsylvania Law School now has an endowed chair professorship named after him, "the Robert Mundheim Professor of Law," which is currently held by Dr. Amy Wax. Mundheim is a member of the Board of Trustees of the American College of Governance Counsel, an American honorary association of lawyers widely recognized for their achievements in the field of governance, and on the Board of Trustees for the Curtis Institute of Music. He has served as a Director of Commerce Clearing House, Inc., First Pennsylvania Bank, CoreStates Bank N.A., a member of the Board of Overseers of the University of Pennsylvania Law School, Benjamin Moore & Co., eCollege, Inc., and Hypo Real Estate. He has also served as a Board Member of the University of Pennsylvania Law School and the Salzburg Seminar, as President of the American Academy in Berlin, and as Vice-Chairman, Governor-at-Large, and Member of Executive Committee of the National Association of Securities Dealers.
