Doctor: Peter Capaldi (Twelfth Doctor)
Michelle Gomez – Missy
Jennifer Hennessy – Moira
Corrado Invernizzi – Cardinal Angelo
Joseph Long – The Pope
Ronke Adekoluejo – Penny
Ivanno Jeremiah – Rafando
Francesco Martino – Peiro
Alana Maria – Pentagon Woman
Laurent Maurel – Nicolas
Jamie Hill – Monk
Tim Bentinck – Voice of the Monks
Directed by Daniel Nettheim
Written by Steven Moffat
Produced by Peter Bennett
Executive producer(s) Steven Moffat, Brian Minchin
Incidental music composer Murray Gold
Series Series 10
Length 49 minutes
Originally broadcast 20 May 2017
The Doctor remains blind ("Oxygen") and wears his sonic sunglasses to provide a limited form of sight while hiding his condition from Bill. He receives an email entitled Extremis that he views through his glasses.
The Doctor is met by the Pope and members of the Holy See to help deal with a recently-translated text called the Veritas, that causes readers to commit suicide. The Doctor takes Bill and Nardole to a secret library inside the Vatican. They find that a translation of the Veritas has been emailed to CERN. Bill and Nardole discover a portal leading to a hub of other portals, linked to CERN and the White House, among other places. Meanwhile, the Doctor temporarily regains his sight using Time Lord technology and tries to read Veritas, but is forced to flee into a second portal with the translation when the skeletal, corpse-like Monks appear. He is unable to read the Veritas before again losing his sight.
Bill and Nardole enter the portal to CERN, finding all the scientists are prepared to kill themselves. A scientist demonstrates that every time he asks them for a random number, they, along with the other scientists, all say the same one. The two flee back to the hub. Nardole realises the portals are actually computer projections, and when he steps out of the projections, he disappears. A distraught Bill follows a trail of blood through a portal, finding herself in the Oval Office of the White House, where the Doctor is waiting. The Doctor explains that Veritas describes a "demon" planning to invade Earth by creating detailed simulations of it to practice invasion. Simulacra within these "shadow worlds" can discover the false reality as they can only come up with pseudo-random numbers due to the nature of computers, leading them to "commit suicide" to escape the simulation. He reveals that he, Bill, Nardole and everybody else are simply simulacra within a simulation. A Monk appears, and Bill disintegrates the same way Nardole did. The Doctor, aware he is a simulation, tells the alien that the Earth will be ready as he has been recording everything through his sonic glasses and emails the recording, titled Extremis, to his real-world self.
The real Doctor finishes Extremis, and turns to the Vault behind him, revealed in flashbacks to hold Missy whom he had spared from execution but vowed to keep locked away for one thousand years. Through the Vault doors, he asks Missy for her help to fight the upcoming invasion.