Cohen was born in Lake Forest, Illinois, and grew up in Chicago's North Shore suburb of Glencoe. He received his BA from Tulane University in 1990. His father, the negotiator Herb Cohen, grew up with the broadcaster Larry King; Cohen worked on King's CNN show for a short time after graduation. His sister, Sharon Cohen Levin, is an Assistant United States Attorney of the Southern District of New York.
An admirer of the works of journalists A.J. Liebling, Ian Frazier and Joseph Mitchell, Cohen took a job as a messenger at the offices of The New Yorker magazine, where he published twelve stories in the "Talk of the Town" section in eighteen months. After working as a reporter for The New York Observer, Cohen joined the staff of Rolling Stone in 1994. Since 2007, he has been a contributing editor at Vanity Fair.
Cohen published his first book Tough Jews...a non-fiction account of the Jewish gangsters of 1930s Brooklyn...in 1998. In The New York Times, writer Vincent Patrick called the book "marvelous," with "writing good enough to cause one, at times, to reread a page in order to savor the description."
His second work, The Avengers: A Jewish War Story (2000), follows a group of anti-Nazi partisans in the forests of Lithuania at the close of World War II. The book was excerpted in Newsweek. Publishers Weekly called the non-fiction work "a terrific narrative of courage and tenacity," and The Washington Post called it "a tremendous story."
Cohen's 2006 book Sweet and Low is a memoir about the creation of the artificial sweetener, a product invented by Benjamin Eisenstadt, the author's grandfather. Newsweek praised the book as "sad, true and hilarious"; The Washington Post called it "superb," and "a wildly addictive, high-octane narrative". Writing in The New York Times, critic Michiko Kakutani called the book "a classic"..."a telling...and often hilarious...parable about the pursuit and costs of the American Dream."
On August 8, 2009, Cohen is scheduled to publish Israel is Real: An Obsessive Quest to Understand the Jewish Nation and its History. In The New York Times Book Review, the writer Tony Horwitz said the book "accomplished the miraculous. It made a subject that has vexed me since childhood into a riveting story."
On February 26, 2007, Paramount Pictures announced it had closed a deal to produce The Long Play, a screenplay Cohen had written for Mick Jagger and director Martin Scorsese, with Scorsese directing.