The Doctor turns bank robber when he is given a task he cannot refuse – steal from the most dangerous bank in the cosmos. With the help of a beautiful shape-shifter and a cyber-augmented gamer, the Doctor and Clara must fight their way past deadly security, and come face-to-face with the fearsome Teller – a creature of terrifying power that can detect guilt.
The Doctor is trying to convince Clara to come with him for a day of sightseeing in the TARDIS as she prepares for a date with Danny Pink, when the TARDIS phone begins to ring. Despite Clara’s protests, the Doctor answers. Suddenly, they find themselves in a strange chamber with two other people: Psi, a hacker with an augmented brain; and Saibra, a mutant humanoid with the ability to shapeshift. They listen to a recording of their own voices, revealing that they agreed to wipe their own memories. They discover a briefcase left by a shadowy person named “The Architect”. The briefcase contains plans to rob the impregnable vaults of the Bank of Karabraxos. The group takes tools provided in the case and flee the room (inside the bank itself) as guards arrive. Stranded and with no memory as to why they agreed to rob the bank, the foursome agree to follow the Architect’s instructions. As they work through the plan, Psi reveals that he’d previously erased his own memories in his cybernetic hardware to protect his loved ones. Saibra also confesses to the Doctor that she finds her shapeshifting ability a curse; she immediately changes whenever she touches another person, preventing her from being trusted by others or having romantic relationships.
The group works its way back into the main floor of the vault, with Saibra using the identity of a bank customer to get them in. There, they witness another bank customer being accused of “guilty thoughts” by the bank’s Head of Security, Ms. Delphox. She brings in an alien creature named The Teller to scan the customer’s brain and confirm his guilt, at which point the Teller uses its psychic abilities to destroy the customer’s brain. The Doctor, Clara, Psi, and Saibra reluctantly continue to follow the Architect’s plan and find more briefcases with useful items as they get closer to the main vaults. One case contains six mysterious devices that the Doctor claims he doesn’t recognise. Saibra challenges him on this, and he tacitly admits that they appear to be disintegrators. The plan requires them to pass through the cage where the Teller is kept in hibernation. The Doctor realises that because the Teller can sense guilt, they had undergone the memory wipe to minimise the chances of their being detected. As they cross the cage, the Teller picks up on Clara’s brainwaves and stirs. The Doctor helps Clara break out of the Teller’s scan, but Saibra is caught within it instead. The Doctor gives her one of the disintegrators and assures her it’s painless. She uses it to escape the Teller’s scan at the cost of her own life. Psi is outraged at the Doctor’s detached reaction to her death, but they continue on to complete the mission.
As they continue to the vault, they discover the Teller chasing after them. Psi stays behind to open the vault, but when Clara is cornered by the Teller, he offers himself as a distraction to save her. Psi opts to use his disintegrator rather than die by the Teller’s scan. The Doctor and Clara push on and reach the main vault. One lock remains in place, and the Doctor cannot bypass it. Just then, a solar storm begins that causes the last lock to be released. The storms’s timing causes the Doctor to finally understand – this is a time travel heist. The team was sent back in time to the precise moment of the storm, as this was the best opportunity to access the main vault. Inside the vault, they discover two safe boxes indicated by the Architect. The first contains a device capable of restoring Psi’s lost memories, and the other contains a serum that would stabilise Saibra’s DNA, allowing her to touch people without shifting. The Doctor determines that the item he is meant to find is in the personal vault of Director Karabraxos. However, before they can break in, the Doctor and Clara are captured and taken to Ms. Delphox’s office. She examines the items they removed from the vault before being summoned away. After she leaves the room, the two guards reveal themselves to be Psi and Saibra. The disintegrators were actually teleporters, and the pair reveal that there is a ship in orbit ready to take them offworld. Psi also informs the Doctor that the TARDIS is there, waiting for him. The four head to the Director’s vault.
They break into the vault and are startled to meet Madame Karabraxos, who looks exactly like Ms. Delphox. Ms Delphox turns out to be one of several clones of Madame Karabraxos to help her with administrative matters. Madame Karabraxos orders the Teller dispatched to the vault, along with the destruction of the Delphox clone. The Doctor makes an offhand remark about Madame not liking her own clone. In doing so, he finally understands, from his prior conversation with Saibra, who The Architect is. Karabraxos packs some valuables in a case and begins to leave to escape the intensifying solar storm. The Doctor gives her his phone number and tells her to call him when she is very old and filled with regret. She leaves, and the Teller arrives. The Doctor surrenders to the Teller’s scan, hoping it will remove the earlier memory block. As the Teller scans him, he remembers the events from before: when an elderly, dying Madame Karabraxos called the Doctor and told him of her one big regret. In a montage, the Doctor is then shown setting up the heist – he is the Architect. The Teller sees that the Doctor is actually there to help and releases him from the scan before using its abilities to open another vault door. Inside is another of the Teller’s species – its mate, kept prisoner to force the Teller’s services. The Doctor rescues all six of them with the teleportation devices, and takes the two aliens to a planet with no thought pollution to live out their lives peacefully. He then takes Psi, Saibra and Clara to get dinner before returning everyone to their homes. The Doctor drops Clara off and leaves, reflecting on how impressive robbing a bank is for a date.