Stephen Colbert appeared on The Late Show with David Letterman to discuss the upcoming changing of the guard and make a few jokes at his own expense.

When Letterman steps down as host of The Late Show next year, Colbert will be his replacement. So naturally the two have a lot to talk about. Colbert appeared on Letterman's show Tuesday night, mostly joking about the big change and keeping things lighthearted and funny. Colbert looked excited and nervous to be there, sort of like he always does in these types of situations. That's probably one of the things that makes him so likable—he actually seems overwhelmed and flattered to be in his position.

Letterman told Colbert he looked right at home sitting on the set, which got a huge round of applause from the audience. Here's a portion of the interview, via E! News:

"I'm going to do whatever you have done," Colbert told Letterman, which prompted the host to immediately respond, "No, you don't want to do that."

"Really, no?" Colbert asked. "It seems to have gone pretty well, Dave."

"It's gone…on," Letterman said.

"Well, obviously I'm thrilled and honored to be taking over for you," Colbert exclaimed.

"Well, I'm thrilled as well," Letterman told him. "In a situation like this—Paul and I have been doing this for a long, long time—they could have just as easily hired another boob like me. But they didn't, they hire a guy..."

"They hire a boob like me," Colbert jokingly interjected.

"No, no no no," Letterman began before Colbert continued, "Every boob is like a snowflake, Dave. We're all unique in our own way."