Professionally hilarious people, Mr. Stewart included, aren’t necessarily funny when they talk about themselves. They needn’t be, and this book seeks a serious understanding of everything about him, especially the thinking that shaped the show. But Mr. Smith lets hero worship and repetition slow the book’s momentum. And doses of snark from embittered ex-staffers sound like exactly what they are. Different editing priorities — filling in gaps, cutting out overlaps, keeping in mind a more general audience — would have made for a book that caught more of the lightning of “The Daily Show.”

Image Chris Smith Credit... Lila Marooney

So this otherwise detailed book (want to know Mr. Stewart’s opinion of the White House’s M&Ms?) requires a lot of acrobatics from Mr. Smith. He omits transcript material that’s important to the show’s history. For instance, he cites Mr. Stewart’s best-known disembowelings of guests or interviewers Mr. Stewart has found morally repugnant but doesn’t describe what was said. The Stewart rogues’ gallery includes Jim Cramer, Judith Miller, Bill O’Reilly, Tucker Carlson on “Crossfire” — though his equally memorable ambush of Chris Matthews goes unmentioned. It would have been worth the extra space to remind readers what Mr. Stewart sounds like when he’s in a cold fury. Or a heated one. That’s how Mr. Stewart describes a private showdown with Roger Ailes in which, accusing Mr. Ailes of disseminating “bile,” he said, “Kudos to you for poisoning people while they don’t even realize it.”

The book attests to how well loved Mr. Stewart is by most of those who’ve worked for him — although there have been angry exceptions, and the grousing is included here. (Is it underplayed? Hard to tell when a writer has been given an all-access pass.) It also features some of the show’s breakout stars in candid mode, with the bulk of the funny stories swirling around Mr. Colbert in his early years. Mr. Colbert sounds like the most fearless of the correspondents when it came to getting interviewees to answer outrageous questions — and he was the first of them to be sued. His classic advice, which has been passed down among fellow correspondents: Check your soul at the door. Spend your per diem, preferably by drinking it. You can always eat free cereal in the break room when you get back to New York.

Among behind-the-scenes personnel, Rory Albanese is one of the best raconteurs. Mr. Albanese was with the show early, ran the video research department for a while (the show’s expertise with video clips is sensational, and would have warranted more space here), graduated to executive producer’s rank and became showrunner for the underrated “The Nightly Show With Larry Wilmore.” About the constant adulation “The Daily Show” began to receive, Mr. Albanese says: “I’m not diminishing people’s love of it, but we never walked around that building saying ‘We’re doing it, guys! Truth to power!’ We were just coming in every day and like, ‘What’s a fun thing to talk about on the show tonight?’”