Smith taught at Youngstown State University, Iowa State University, and the University of Wisconsin. He taught as a Fulbright Professor on numerous occasions. He also taught United States history in Japan, at Ochanomizu University and the University of Tokyo from 1954 to 1955. In 1976, he taught a pioneering, uncensored American history course at Moscow State University, returning to the Soviet Union to teach at Moscow in 1982 and at Leningrad State University in 1991. He also taught as an exchange professor at the University of Beijing in 1983 and 1988. Smith later served as president of the Fulbright Association. In 1968, Smith joined the faculty of the Department of History at the University of Maryland. He wrote well-received biographies of Missouri Senator Thomas Hart Benton, presidents James Buchanan, Zachary Taylor, and Millard Fillmore, and Maryland politico Francis Preston Blair. He became a professor emeritus at Maryland in 1990. Smith ran unsuccessfully as the Democratic challenger to Republican incumbent United States Senator Bourke B. Hickenlooper of Iowa in 1962. He received an endorsement from President John F. Kennedy and among his campaign workers was future U.S. Senator Tom Harkin. Nevertheless, he was narrowly defeated. Smith served as Lyndon B. Johnson's Iowa campaign manager in 1964, and ran again for Senate as the Democratic challenger to Jack Miller in 1966. He was later appointed by President Jimmy Carter to the U.S. Foreign Scholarship Board.