ELEMENTARY: Watson and Sherlock investigate the murder of a ballerina in an episode entitled "Corpse de Ballet." (Jeff Neumann/CBS)

Figure skating, snowboarding and women’s freestyle skiing are covered on tonight’s “XXII Winter Olympics 2014 Primetime” (NBC at 8 p.m.), which begins with the men’s and pairs short programs in the Olympics’ first-ever figure skating team event.

After last night’s “Hollywood or Home” redemption round on “American Idol” (Fox at 8), the remaining contestants go on to the notoriously tough “Hollywood Week” in this one-hour episode.

Sheldon is lured into Valentine’s Day plans with Amy when she talks him into a romantic getaway to Napa Valley on “The Big Bang Theory” (CBS at 8), while Leonard and Penny have a far less romantic day with a visit to the vet with Raj’s dog.

“The Taste” (ABC at 8) puts the eight remaining chefs up to a dessert challenge to highlight ingredients like fruit and sweet and savory combinations. Chef Christina Tosi plays guest judge for the battle that will eliminate two competitors and send the remaining six to the semifinals.

The story of a woman who met a strange, combustible fate in St. Petersburg, Fla., is examined on “Mysteries at the Museum” (Travel at 9), along with a box that was used in a shocking experiment.

A serial dater comes to Patti’s crew on “The Millionaire Matchmaker” (Bravo at 9) and so does a Tennessee native with country values, all while Patti plans a Valentine’s Day ball.

To fuel her gambling, a mom commits insurance fraud by saying her son has cancer, so Keegan on “Rake” (Fox at 9) has to search for an approach to appeal to the jury’s emotions.

A ballerina is murdered and Holmes puts the focus on a professional dance company to try to solve the case on “Elementary” (CBS at 10). Then, Dr. Joan Watson is on a case involving the possible abduction of a homeless veteran.

Actor Michael Keaton comes to the “Late Show With David Letterman” (CBS at 11:35), with music from the Flaming Lips plus Sean Lennon.

For his last show as host, Leno’s got Billy Crystal on “The Tonight Show With Jay Leno” (NBC at 11:35), with a musical performance from Garth Brooks.

“Jimmy Kimmel Live” (ABC at 11:35) welcomes “The Monuments Men” cast, which includes Matt Damon, George Clooney, Bill Murray, Cate Blanchett and Bob Balaban.

— Rachel Lubitz