He received bachelor's degrees in music and journalism from Syracuse University in 1976. He began freelancing as a critic and music feature writer for The New York Times in 1977, and joined the paper's staff in 1991. Before joining the Times, he was a contributing editor to High Fidelity and Keynote magazines, and a frequent contributor to Guitar Player, Keyboard, Pulse and other publications. He was also the first music critic for the New York Observer. Kozinn has written a number of books, including Guitar: The History, the Music, the Players (1984), Mischa Elman and the Romantic Style (1990), The Beatles (1995) and a useful volume on  Classical Music: A Critic's Guide to the 100 Most Important Recordings (2004)..
Kozinn joined the faculty of New York University in 2004, where he has taught courses in music criticism, Baroque music literature and the Beatles. He also taught a course in the history of musical interpretation at the Juilliard School.
On September 3, 2012, Norman Lebrecht broke the story that Kozinn would no longer be a music critic for The New York Times and that he would now be demoted to a general "culture reporter." A protest to the Times was instigated, with many musicians, critics, and readers adding their voices. Kozinn takes exception to Norman Lebrecht's use of the word demotion. Although his preference was to remain a classical music critic, he as well as the Times did not consider Allan Kozinn's reassignment as a demotion. He has taken no cut in salary, hours or benefits, and his job title remains Classical Music Critic.
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