Late Show, on CBS, weeknights at 11:35PM
CBS; Wikipedia

David Letterman (1993-2015)
IMDb; TV.com; TV Tropes; Wikipedia

Prior to this, I never had a chance to watch a late night talk show. (Unless you count something like "The Pat Sajak Show," and, you know... why would you?) Anyway, back when this came on, in 1993, the only major network I had access to was CBS. David Letterman had previously hosted Late Night, on NBC, but obviously, I'd never had a chance to see that. So I didn't really know Letterman, or anything, but even so, I was excited when this show started, and I enjoyed it, and watched it fairly often for the first few years. I hardly ever watch it anymore, but I'm sure it's still good. Um... the bandleader/sidekick is Paul Shaffer. And... I remember back in the day liking some of the people who appeared regularly (Rupert Jee, Mujibur and Sirajul). And the Top Ten lists are always fun. And I fondly recall the show's coverage of the 1994 Olympics. And stuff. Letterman retired in May 2015, but sadly, I didn't have a chance to see his final episode (nor any episodes for quite awhile before that).

Stephen Colbert (2015-present)
A.V. Club; CBS; Global; IMDb; TV.com; Wikipedia

In September 2015, Stephen Colbert (formerly of Comedy Central's The Colbert Report) took over as host. (And it seems the word "The" was added to "Late Show.") I'd really like to check it out, but I don't know if or when I'll get a chance, because... reasons.