Despite NBC’s controversial decision in the early ’90s to tap Jay Leno as Johnny Carson’s replacement for the Tonight Show, it was David Letterman who would ultimately inherit Mr. Carson’s crown as the undisputed king of late night. In the decade before Mr. Carson’s retirement, NBC’s Late Night with David Letterman revitalized the evening talk-show formula and introduced a new generation of comedians and humorists to TV audiences. When Mr. Leno took over Tonight in 1993, Mr. Letterman took his talents to CBS, and redubbed his hour The Late Show with David Letterman. During his 20 years with CBS, Mr. Letterman has continued reinventing the format for late-night TV, making it sleeker, smarter and sexier. Mr. Letterman’s style, sense of humor and body of work set the tone for the next generation of late-night hosts, from Jon Stewart to Conan O’Brien. And while he might have been born in Indianapolis, Mr. Letterman’s irreverent, acerbic take on the news and quick repartee with guests are quintessentially New York. His tenure at the historic Ed Sullivan Theatre has turned the venue into a must-visit city landmark. A list of Mr. Letterman’s writing staff over the years reads like an all-star team of American comedy. From George Meyer, godfather of The Simpsons writing room, to veteran SNL writer and producer Jim Downey, Mr. Letterman hand-picked a generation of men (and a few women) who would come to define the future of American comedy writing. While spawning a brand of comedy as ubiquitous as the gap between his front teeth, that same smile greets us at 11:30 each weeknight. Through five presidents and one emergency quintuple bypass surgery, Mr. Letterman has surpassed Johnny Carson as the longest-running American talk-show host and has become an enduring American icon in his own right.