Downsizing

In the TARDIS, The Doctor is returning Clara to the present day after an adventure, with Clara still maintaining the lie that her boyfriend, Danny Pink, is fine with her traveling with The Doctor.

When the TARDIS materialises, The Doctor finds that something is draining energy from the TARDIS, and the mystery energy field has caused them to land in Bristol rather than London. They also discover that it has caused the exterior of the TARDIS to shrink in size.

The Doctor stays inside the shrunken TARDIS to figure out what is going on and discover the source of the power drain while Clara looks around outside. She soon encounters a local community service crew, working at repainting over graffiti in the area. Rigsy, one of the workers who was also responsible for some of the graffiti, tells Clara about the strange case of locals disappearing, and of the strange painted murals in a nearby pedestrian tunnel.

The Doctor and His Smaller TARDIS

When Clara returns to where the TARDIS landed. she finds that its exterior has shrunk even further, trapping The Doctor within as he is now unable to fit through the tiny doors. The Doctor hands Clara his psychic paper, sonic screwdriver, and an audio/visual earpiece so he can keep in touch with her. He then has her carry the TARDIS with her to where he has traced a large source of energy.

Clara poses as 'Doctor Oswald' and gains the confidence of Rigsy who helps her, despite The Doctor's scepticism about any help Rigsy can provide. Inside the flat, of the latest disappearance, they find nothing but a strange desert mural on the wall. Rigsy gains help from a police officer, PC Forrest, to gain access to the flat of the first known missing person. The Doctor instructs Clara to tear out the walls, believing the energy source to be within them. While they work, PC Forrest is sucked into the floor in another room, out of view of Clara and Rigsy. When they react to her screams they discover that she has disappeared. They look around the room and find another strange mural. The Doctor realises it's likely to be PC Forrest's nervous system, and he deduces that the first mural they saw, inside the flat of the latest disappearance, was a close-up of that victim's human skin.

Doctor Oswald

The Doctor warns them they are dealing with entities that live in two-dimensions and that the missing people are victims of the creatures' experiments in understanding the third dimension. As Clara and Rigsy watch, they see the creatures move about the walls and floor and start to move towards them. They then find themselves trapped in the room when the doorknob becomes flattened into two dimensions. Realising that the walls and floor are dangerous the two scramble onto a hanging seat to protect themselves, and then swing through the nearby window to escape.

During this, Clara receives a call from Danny, who has been waiting for her in London. She manages to avoid questions of her whereabouts and quickly hangs up. However, The Doctor, who is listening in to her conversation, recognises that Clara has lied to him about Danny accepting her continued travels in the TARDIS.

Clara and Rigsy return to the rest of the community service group, who are about to paint over the murals in the pedestrian tunnel. The Doctor realises that the images are disguises for the creatures and after one of the services workers is taken over by the creatures, Clara leads the rest away with the creatures chasing them. They take shelter in a nearby engine repair warehouse, where The Doctor helps Clara try to communicate with the creatures using mathematics. When another worker is taken, Clara and the surviving members flee into a disused subway tunnel.

Clara and Rigsy

As they explore, they find that the door of their only escape route flattened into two dimensions by The Boneless. They also soon realise that the creatures have learned how to manifest themselves in three dimensions by drawing even more power from the TARDIS, taking the forms of the missing persons who start to give chase to the survivors. The Doctor provides Clara with a device to restore the dimensions of the door, and they just manage to escape. However, in the chaos, the TARDIS is shrunk further and falls down a shaft on to an active railway line. The Doctor is forced to activate the TARDIS' siege mode to protect it from an oncoming train, but without power, he is unable to return it to normal or to communicate with Clara. Clara uses the sonic screwdriver to stop an out-of-service train, and they attempt to ram the creatures, who are advancing towards them in the railway tunnel, so as to gain time for her to get back in contact with The Doctor. However, the train is simply transformed into two dimensions and appears on the tunnel wall.

As they escape, Clara finds the TARDIS, now looking like a plain Gallifreyan cube, lying on the track, and takes it with her. Taking shelter in a disused office space, Clara comes up with a plan to provide energy to the TARDIS by having Rigsy paint a fake access door on the back of a large poster, so that when the creatures attempt to pull the door into three dimensions, they instead feed their energy into the TARDIS.

Clara's plan works and the TARDIS is returned to normal allowing The Doctor to escape and so take control. Realising they have no interest in peace, The Doctor uses his sonic screwdriver to stop the creatures, whom he dubs 'The Boneless', by sending them back to their dimension with a warning to those who survive the trip to never return. The Doctor, using his TARDIS, then returns everyone to the surface safely. While saying good-bye to Rigsy, and the other surviving members of the community service group, Clara rejects a call from Danny, catching The Doctor's attention. He notes that she enjoyed 'playing The Doctor' for the day.

Unbeknown to The Doctor or Clara we see Missy, seated in a darkened room, watching Clara on hand-held screen. It appears that Missy has been watching the recent events. Missy is then heard to say, with regard to Clara, that she has 'chosen well'.