It started much like the way it ended for David Letterman.
There he came, striding onto the stage at the Ed Sullivan Theater on Monday night, to a standing ovation and a chorus of chants of “Da-vid! Da-vid!”
The only difference this time was that Mr. Letterman, in a full gray beard, was a guest of “The Late Show,” and Stephen Colbert, its host since 2015, led him to a chair that was not behind a desk.
“Stephen,” Mr. Letterman said as he sat down. “Control your people!”
Mr. Letterman’s appearance on “The Late Show” — the series he began for CBS in 1993 and hosted until Mr. Colbert replaced him — brought some resolution to one of the odder mysteries in show business: Why wouldn’t he visit with his successor?
Mr. Letterman has been no stranger to the limelight since he stepped down from his late-night gig. He hosts his own Netflix long-form interview show, “My Next Guest Needs No Introduction,” and he has visited plenty of other shows. He has done Jimmy Kimmel’s ABC show several times; Seth Meyers’s late night show; Ellen DeGeneres’s daytime talk show; Howard Stern’s radio show; Dax Shepard’s podcast; Marc Maron’s podcast; Conan O’Brien’s podcast. He even did the Busy Philipps podcast.
All of those appearances made his absence from Mr. Colbert’s show even more conspicuous. After all, it is something of a television tradition for grand eminences of late night to visit their successors.
Jay Leno has joined Jimmy Fallon on “The Tonight Show.” Jon Stewart visited his successor, Trevor Noah, on “The Daily Show.” Mr. Letterman, then at rival CBS, visited Mr. O’Brien on “Late Night,” the 12:30 a.m. NBC show that he had created over a decade earlier.
Was being back at the Ed Sullivan Theater too much to bear for Mr. Letterman?
Was it the fact that it took Mr. Colbert less than two years to become the most-watched host in late night, a designation that eluded Mr. Letterman for most of his run?
Or was something else at play?
In a 2015 interview with The New York Times, Mr. Letterman said he had initially been bothered that he wasn’t consulted about who would replace him. He also seemed surprised that Mr. Colbert had been selected so quickly after Mr. Letterman announced that he was retiring.
“They didn’t have to put much thought to it, did they?” he said in 2015. “I think it was the very next day.” (Mr. Colbert was hired a week later.)
During his appearance on Monday, which took up more than 20 minutes of airtime, Mr. Letterman and Mr. Colbert avoided the topic. Instead, Mr. Letterman discussed, among other things, visiting CVS pharmacies, his son going off to college, and how he made his way into the studio on Monday.
“I came to the show this afternoon, and people were saying, ‘Yes, may I help you?’” Mr. Letterman said. “And I said, ‘I’m Ed Sullivan.’ Got me right in.”
Mr. Colbert asked Mr. Letterman if he missed anything about hosting a late night show.
“I miss everything,” Mr. Letterman replied. “Mostly, it’s fun. Very few things in life provide one the opportunity — and I can’t speak for you on this topic — but for me, if you muck one up, 24 hours later, you get to try again.”
The ice may have broken a few weeks ago when Mr. Letterman was a guest on “Strike Force Five,” a podcast that several of the current late-night hosts, including Mr. Colbert, started during the Hollywood writers’ strike. During the interview, Mr. Colbert used the occasion to clear the air about how he had been hired.
Over several minutes, Mr. Colbert explained that CBS executives first approached him in 2013 to discuss the possibility of replacing Mr. Letterman. At the time, Mr. Colbert said, he wanted assurances from CBS that Mr. Letterman was aware of this meeting. He was told that the network had Mr. Letterman’s blessing to meet with people.
Six months later, in April 2014, Mr. Letterman announced that he would step down from “The Late Show.” But, Mr. Colbert explained in the podcast, he then received an odd message that made him wonder if Mr. Letterman had actually known about the outreach.
Mr. Letterman said on the podcast that CBS executives might have thought he was considering retirement — but that he had never explicitly told them to begin a search for his replacement.
“I’m certain that that part didn’t happen,” he said.
Mr. Letterman then recalled on the podcast how he had found himself in a similar situation years earlier when NBC executives wanted him to host “The Tonight Show” part time with Johnny Carson. When Mr. Letterman found out that Mr. Carson was not aware of the arrangement, he declined to participate.
As Mr. Letterman’s “Late Show” appearance reached its end, he made a request of Mr. Colbert: Could he take a seat behind his desk? Mr. Colbert immediately sprung up, and gave up his chair for Mr. Letterman.
With Mr. Letterman behind the desk, Mr. Colbert had a question.
“Very few people know what it’s like to host one of these things,” he said, gesturing to the backside of his desk. “What do you think of my supplies? Was that anything like you had down there?”
“What?” Mr. Letterman replied. “All this weed?”