Wallace, one of the original correspondents and hosts of "60 Minutes," which started in 1968, died Saturday night in New Haven, Conn.
"His family was with him," said "Face the Nation" host Bob Scheiffer, who announced Wallace's death Sunday. The nature of his illness was not reported.
Wallace was best known for a signature interviewing technique, asking the tough and often irreverent questions, The New York Times reported Sunday. He characterized himself as "nosy and insistent."
He asked the Ayatollah Khoumeini if he was crazy. He asked mobster Mickey Cohen, "How many men have you killed, Mickey?" CBS News reported.
Wallace semi-retired in 2006, often returning to "60 Minutes" to interview key figures like Mitt Romney, Mahmoud Ahmadinejad and Jack Kevorkian. His final interview appeared on the newsmagazine in January 2008 when he sat down with baseball legend Roger Clemens.
"It's astonishing what you learn and feel and see along the way," Wallace said of his career in journalism. "That's why a reporter's job, as you know, is such a joy."
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