Born in Ferriday, Louisiana, Smith graduated as a Rhodes Scholar from Oxford University (Merton College) in September 1939. He immediately went to work for United Press as their London reporter and in January 1940 was sent to Berlin where he soon moved to CBS. He visited Berchtesgaden and interviewed many of the most prominent Nazis, including Adolf Hitler, Heinrich Himmler and Joseph Goebbels. In December 1941 he was the last American reporter to leave Berlin, being expelled by the Nazis. A book based on his experiences reporting from Berlin after William L. Shirer's departure, Last Train from Berlin, became an American best-seller.
Unable to leave Switzerland, Smith reported what he could when the Swiss government would let him. After the liberation of France in 1944, Smith reported on the war effort on the frontlines of Europe for CBS News. He was by then a significant member of the "Murrow Boys" (after Edward R. Murrow) that made CBS News the dominant broadcast news organization of the era. In May 1945 he returned to Berlin to recount the German surrender.
After the war Smith continued to work for CBS, presenting various documentaries and chairing the first television debate between John F. Kennedy and Richard Nixon. In 1962 he lost his job at CBS over his liberal views of the civil rights movement. Smith moved to ABC where he remained until 1979, being co-anchor on the Evening News from 1969.