Stewart also recalled that Colbert worried at first that the “Report” might not be sustainable, and says he kept pointing out, “ ‘I don’t know anyone more interesting than you. You know so much about so many different areas.’ ” Stewart went on: “I’m not at all surprised that the show is good — he’s amazing at it. He’s able to weave a character in a way that’s never been done on television before — rendering this fictional character in 3-D, live, in such a way that he’s still able to retain his humanity.” The extra dimension, he explained, is the other Colbert, the real one. “The third dimension is him. That’s the thing we started to see here. He is so interesting, smart and decent. He’s a good person, and that allows his character to be criminally, negligently ignorant.”

The Colbert on-screen persona is actually less rigid than it used to be, and Colbert can dial it up or down as he chooses. There is now more of a winking quality to the act, a sense that we’re all in on the joke. And in the last part of the show, when Colbert typically leaps up from his desk and bounds across the set to a table in front of a fireplace with the Latin motto “Videri quam esse” (“To seem to be, rather than to be”), where he interviews a guest about a new book or movie, he usually tamps the character down enough to allow the guest a few minutes to get his or her own message across.

When Harry Belafonte was on recently, for example, Colbert cut him some admiring slack and even joined in singing “Jamaica Farewell,” instead of ripping into Belafonte for being a lefty agitator. A month earlier, in September, the Colbert presence was so friendly and relaxed that Al Gore, on to talk about the Climate Reality Project, forgot himself and violated the show’s cardinal rule — he broke the fictional wall. Talking about Keith Olbermann, Gore said, “He scares Fox News, and he scares your character, as he should.” “My character?” Colbert cried in mock bewilderment.

Colbert is not Ali G. He doesn’t sandbag the unsuspecting. And he is particularly careful to visit guests beforehand in the green room and prepare them for what’s going to happen. When John Lithgow was on recently to promote his new memoir, “Drama,” Colbert warned him that his character would become the biggest jerk Lithgow had ever met. “Just pretend I’m the drunk in a bar who won’t shut up,” he said.

But in the early days of the show, when Colbert’s persona was more earnest and deadpan, and when people were less used to it, there were some memorably strange and awkward moments. In 2005, the show’s first season, Colbert interviewed a humorless and expressionless Barney Frank, who said, “Ignorance does not offend me” when Colbert seemed surprised to discover that he was gay. A moment later Frank threw up his hands and declined to proceed, saying that the questioning had become too dumb to take seriously.

But easily the most awkward moment in Colbert’s career, and also in many ways a defining one, was his appearance at the White House Correspondents’ Dinner in 2006. Mark Smith, an A.P. reporter who, as head of the correspondents’ association, was responsible for booking the talent, admitted later that he wasn’t all that familiar with the show, which was only three months old when he approached Colbert. Neither, to judge from video of the event, were many in the audience. Colbert got up and addressed the president, saying: “I stand by this man because he stands for things. Not only for things. He stands on things. Things like aircraft carriers and rubble and recently flooded city squares. And that sends a powerful message: that no matter what happens to America, she will always rebound — with the most powerfully staged photo-ops in the world.”

Never cracking a smile or breaking out of character, he went on to praise Bush for believing “the same thing Wednesday that he believed on Monday, no matter what happened on Tuesday” and to point out that the administration wasn’t sinking but soaring. “If anything,” he said, “they are rearranging the deck chairs on the Hindenburg.” Nor did he leave out the correspondents themselves. “Over the last five years you people were so good,” he said. “Over tax cuts, W.M.D. intelligence, the effect of global warming: we Americans didn’t want to know, and you had the courtesy not to try and find out.”