What’s On: Letterman’s Mark Twain Prize, Another Acorn TV Winner, ‘Dancing’ and ‘Voice,’ ‘Brave’ winter finale

The Kennedy Center Mark Twain Prize for American Humor (8/7c, PBS, check local listings at pbs.org): Stupid pet tricks. A special all-star Top Ten list. Influential late-night comedian David Letterman has more than earned this honor, the 20^th Mark Twain Prize, and his gracious, self-effacing speech at the end lends a warm afterglow to a night that’s a little bit roast but much more of a tribute. Taped last month at D.C.’s Kennedy Center, the night begins with a rib-tickling two-hander featuring Martin Short and Steve Martin, praising Dave’s spot-on comedic instincts: “What better time than now to insist on looking like a Confederate war general?” The bushy beard comes in for lots of jokes, but the comic lineup is dead serious when it comes to his impact on humor. Admirers include Amy Schumer, Jimmy Kimmel, Norm Macdonald, bandleader Paul Shaffer and last year’s honoree, Bill Murray, in a hilarious bit of performance art. (Another highlight: Fred Armisen and Bill Hader in a Documentary Now! mock remembrance from Dave’s home state in Indiana.) Missing from the final cut: Sen. Al Franken, whose brief comments were excised by PBS so as not to distract from the joy of the event. Which is plentiful.

Late Night in the Age of Trump (9/8c, CNN): In the Letterman special, Jimmy Kimmel jokingly blames the current state of the world on his idol having left TV. Kimmel, Seth Meyers, Stephen Colbert, John Oliver and Trevor Noah are among the unsparing late-night hosts who nightly skewer the current administration, which also takes a weekly beating on Saturday Night Live with Alec Baldwin’s Emmy-winning impersonation. CNN’s Brian Stelter examines the phenomenon and the impact the current president (and his Twitter feed) has had on the state of late-night laughter.

Love, Lies & Records (Streaming on Acorn TV): The delightful comedy-mystery Agatha Raisin only lasted one season, but that series’ star, the warmly appealing Ashley Jensen, is back in another original gem from the streaming service specializing in top-shelf British imports. In this co-production with the BBC, Jensen plays Kate, a registrar who gets entangled in the emotional intrigues of the births and weddings she registers and occasionally presides over, often bending the rules. The fact that her own home life is a bit of a mess, and that an office scandal could endanger her recent promotion, only adds to the enjoyment. The opening episode features a wedding ceremony in a hospice that will move all but the stone-hearted. Here’s something to fill the time between episodes of This Is Us.

Dancing With the Stars (8/7c, ABC): The mirrorball is being readied, because by the end of Tuesday’s live show, one of four couples will walk away with the prize. Former pro/judge Julianna Hough returns for Monday’s finals, featuring a Redemption dance and the all-important Freestyle for the finalists, including Lindsey Sterling, Jordan Fisher, Frankie Muniz and (really?) Drew Scott. One couple will be eliminated at the end of the show, and the final three move on to Tuesday’s final round.

The Voice (8/7c, NBC): The singing competition also moves into its final stage, though there’s still a way to go before crowning a champ, with 12 finalists going into the live performance round. One will be eliminated Tuesday, and typical for the show, will likely be upstaged by Adam Levine and Maroon 5 taking the stage. As if you ever had to ask who the real stars of this show are.

The Brave (10/9c, NBC): The best of the fall’s network military dramas wraps its fall run with a very tense outing, in which the team goes after the terrorist responsible for the beach attack from the beginning of the season. Going inside Tehran, Iran to pull off this sanctioned hit, the special ops agents must improvise when things go awry, leading to a cliffhanger likely to keep fans anxious until the show’s return on Jan. 1.

Inside Monday TV: The Wire‘s Sonja Sohn is back on that acclaimed drama’s home turf, directing the HBO documentary Baltimore Rising (8/7c), about the efforts of community leaders to keep the city from exploding or imploding in the wake of the 2015 death of Freddie Gray while in police custody. … A weeklong binge of the classic Gilmore Girls begins at 10 am/9c on UP, continuing through Sunday. Yanic Truesdale (Michel) hosts, with hourly sweepstakes rewarding fans throughout. … On Fox’s The Gifted (9/8c), Reed (Stephen Moyer) learns secrets from his family’s past while visiting his estranged father. And the Mutant Underground learns there’s a Sentinel Services spy in their midst. … A new emotional trauma affects ABC’s The Good Doctor (10/9c) when Dr. Shaun (Freddie Highmore) witnesses a robbery while grocery shopping.