David Letterman's Late Show on CBS ran for 22 years and represented the apex of the American late-night talk show format. Letterman's influence on comedy — his ironic distance, his structural deconstruction of the talk show form, his Top Ten Lists, his Stupid Human Tricks — shaped virtually every comedian and late-night host who followed him. His interviews ranged from deeply uncomfortable to genuinely revelatory, and his live broadcast on September 17, 2001 — the first late-night show after 9/11 — is remembered as one of the most emotionally significant moments in American television history. Conan O'Brien, Conan's writers, and dozens of other major comedians cite Letterman as their primary influence.

Reference:

Wikipedia: Late Show with David Letterman

https://en.wikipedia.org/wiki/Late_Show_with_David_Letterman