‘GREY'S ANATOMY’: Derek and Amelia work together on a difficult surgery involving conjoined twins at 9 p.m. on ABC. (Eric McCandless/ABC)

The “iHeartRadio Music Awards” (NBC at 8 p.m.) showcase and congratulate the biggest artists and songs from the past 12 months, with Blake Shelton, Drake, Kendrick Lamar, Pharrell, Pitbull, Shakira and Thirty Seconds to Mars all scheduled to perform live.

The 13 remaining chefs split up into teams to prepare the most impressive Southern-inspired menu possible for a sorority’s anniversary party on “Hell’s Kitchen” (Fox at 8).

Sheldon’s childhood hero Professor Proton (played by guest star Bob Newhart) helps Sheldon deal with grief, while Bernadette and Amy consume themselves with their very own “Star Wars Day” on “The Big Bang Theory” (CBS at 8).

When Stefan and Elena are put in imminent danger on “The Vampire Diaries” (CW at 8), Damon suggests going to Caroline’s father’s cottage, where he then insists on playing a game to make Stefan and Elena confess a few of the secrets they’ve been hiding.

Cristina faces a major decision and looks to Meredith for guidance on “Grey’s Anatomy” (ABC at 9), and Amelia and Derek collaborate on a high-profile and dangerous procedure.

In its shortened format, “American Idol”(Fox at 9) boots off one competitor to form the Final 4 and even has time for a performance from Keith Urban.

“Mysteries at the Museum” (Travel at 9) reveals secrets from a lawn chair steeped in history, a failed invention and a dollhouse-like diorama.

Sherlock and his brother Mycroft are forced to work together on “Elementary” (CBS at 10) on a case that could mean life or death for their client.

The medical students investigate why a nanny continues to have hallucinations, while personal medical information on all of the doctors and students is revealed for the safety of their patients on “Black Box” (ABC at 10).

FINALE WATCH: To wrap up “Vikings” Season 2 (History at 10), Ragnar and King Horik return to Kattegat and new alliances are formed.

Actors Andrew Garfield and Mary Lynn Rajskub are on “The Tonight Show Starring Jimmy Fallon” (NBC at 11:35), with music from Chvrches.

Actors and comedians Louis C.K. and Amy Sedaris come to the “Late Show With David Letterman” (CBS at 11:35), with a performance by the Broadway cast of “Rocky.”

Actress Sandra Oh and “Science Bob” Pflugfelder stop by “Jimmy Kimmel Live” (ABC at 11:35), along with a musical performance from Boy George.

Rachel Lubitz