Separated from the Doctor, Clara discovers a new menace from another dimension. But how do you hide when even the walls are no protection? With people to save and the Doctor trapped, Clara goes against an enemy that exists beyond human perception.
On returning Clara to London, the Doctor finds something is draining energy from the TARDIS and they end up in Bristol instead. They find the TARDIS’ exterior size has shrunk as a result of the energy drain, and the Doctor sends Clara out to learn more while he tries to stop the drainage. Clara befriends Rigsy, a graffiti artist now performing community service with a small crew. Rigsy explains several people have gone missing recently, their disappearances memorialized by a mural in a pedestrian tunnel painted by an unknown person. Clara returns to find the TARDIS has shrunk even farther, with the Doctor unable to physically get out. He passes her his sonic screwdriver, psychic paper, and an earpiece to let him communicate with her, and asks her to carry the TARDIS with her as she rejoins Rigsy, taking on the role of “Doctor Oswald” and adopting several of the Doctor’s mannerisms.
At the flat of the latest disappearance (who is shown taken in the cold opener) they find nothing amiss save for a strange mural of a desert on one wall. With help of PC Forrest, they enter the flat of the first disappearance, and the Doctor instructs them to tear out a wall believing the source is within. In the next room, PC Forrest is suddenly absorbed into the floor, and by the time Clara and Rigsy arrive, she is gone. The Doctor is drawn to another wall mural, and realises it is the shape of a human nervous system, suspecting that is the fate of PC Forrest; he concludes the desert mural in the other flat was a close-up of the skin of the last victim. He deduces that they are being attacked by creatures that live in two dimensions, which he later names the Boneless, trying to experiment in understanding the third dimension. The Boneless trap the two in the room by flattening the door handle to two dimensions, but Clara and Rigsy escape through a window using a hanging chair. During the escape, Danny Pink calls Clara as she is late for their meeting in London. The Doctor overhears the call and knows that Clara has lied, both to Danny about discontinuing her travels with the Doctor, and to the Doctor in affirming Danny’s acceptance of her traveling with the Doctor.
Clara and Rigsy race to stop the community workers from painting over the murals in the tunnel, which the Doctor has deduced are disguises for the Boneless. After one worker is adsorbed, Clara directs the rest to a nearby train maintenance yard, and follows the Doctor’s instructions to try to communicate with the Boneless using mathematics. When another worker is taken by the Boneless, they flee into a disused tunnel, finding that the Boneless have blocked their escape route by flattening the door to two dimensions. As they watch, the Boneless begin to project themselves into three-dimensional versions of their past victims and give chase. The Doctor provides Clara a device to unflatten the door, allowing them to escape, but this further allows the Boneless to drain more energy from the TARDIS and shrink it further. It spills out of Clara’s handbag and falls onto an active train track; the Doctor activates the TARDIS’s Siege mode to protect it from harm from an oncoming train, but leaving it powerless to revert out or for the Doctor to communicate with Clara.
Clara is able to stop an out-of-service train and they use it to attempt to ram the oncoming Boneless and give themselves time, but they simply transform it to a two-dimensional image. As they flee, Clara finds the TARDIS, now resembling a Gallifreyan cube, and takes it with her. In a disused office, Clara comes up with a plan, and has Rigsy paint a realistic-looking door on the back of a large poster which they then hang over an open doorway in a tunnel; when the Boneless encounter the fake door, they try to unflatten it with their energy but this instead funnels power back to the TARDIS situated behind the poster. The Doctor uses the energy to restore the TARDIS to normal. Realising they have no interest in peace, the Doctor uses the TARDIS and sonic screwdriver to stop the Boneless, sending them back to their dimension with a warning to those who survive the trip to never return. The Doctor returns everyone to the surface safely. Clara rejects a call from Danny, catching the Doctor’s attention. He notes that she enjoyed ‘playing the Doctor’ for the day.
The episode concludes with Missy, seated in a darkened room, watching Clara’s adventure on a tablet computer. Missy says, with regard to Clara, that she has “chosen well”.