After earning his Phi Beta Kappa key from Brown University and serving as Current Topics Editor for the Yale Law and Policy Review while at Yale, Muller clerked for United States District Judge H. Lee Sarokin in Newark, New Jersey from 1987 to 1988. He then practiced in the litigation department of a private law firm in Manhattan from 1988 to 1990, before joining the United States Attorney's Office in Newark, where he served as an Assistant U.S. Attorney in the Criminal Appeals Division from 1990 to 1994.
After several years of adjunct teaching at Seton Hall Law School while still in government practice, Muller moved to the University of Wyoming College of Law in 1994 to begin full-time teaching, specializing in criminal law and procedure and constitutional law. In 1997, the graduating class named him the Outstanding Faculty Member in the College of Law.
Muller joined the UNC faculty in the fall of 1998. He has published articles in the Yale Law Journal, the Harvard Law Review, and the University of Chicago Law Review, among many other academic journals. His book "Free to Die for their Country: The Story of the Japanese American Draft Resisters of World War II," was published in August of 2001 by the University of Chicago Press, and was named one of the Washington Post Book World's Top Nonfiction Titles of 2001. His second book, "American Inquisition: The Hunt for Japanese American Disloyalty in World War II," was published by the University of North Carolina Press in October of 2007. His most recent book, "Colors of Confinement: Rare Kodachrome Photographs of Japanese American Incarceration in World War II", published by the University of North Carolina Press in association with the Center for Documentary Studies at Duke University, was profiled in the New York Times in June of 2012. It won the Joan Patterson Kerr Book Award from the Western History Association in 2013.
From 2008 through 2011, Muller served at the law school as Associate Dean for Faculty Development. In both 2010 and 2011, he received the Frederick B. McCall Award for Teaching Excellence, voted by the graduating classes.
Muller serves as Chair of the Board of Governors of the University of North Carolina Press and is a member of the university-level Appointments, Promotion and Tenure Committee at UNC-Chapel Hill.
From January of 2012 through December of 2015, Muller served as Director of the Center for Faculty Excellence at the University of North Carolina at Chapel Hill, the campus's faculty development center.