The next morning, at half past six, Rory's dad Brian, wakes them up to tell them that billions of featureless black cubes have appeared everywhere in the world. The street is full of them. While Amy and Rory join Brian in the street, Amy notices the Doctor in the playground opposite, examining a cube. The news channels, too, are full of the story. Some speculate that it is a stealth marketing campaign while experts like Professor Brian Cox declare they are not space debris. They are lifeless and resistant to any kind of testing the Doctor has tried so he takes the TARDIS into the Ponds' house and decides to use their kitchen to cook the cubes.
Rory starts to get dressed for work. The Doctor is amazed that he has a job. Amy tells him they both work: Rory is still a nurse and she writes articles on travel. Amy tells the Doctor that she has been travelling with him, on and off, for about ten years. She is almost thirty. As they speak, a UNIT detachment, led by their scientific advisor, Kate Stewart (daughter of Brigadier Lethbridge-Stewart), arrives at the Ponds' house after an energy spike gives away the position of the TARDIS. Kate recognises the Doctor by his dress sense and a hand held x-ray device that shows his two hearts. She explains that UNIT are baffled by the cubes, too. She has heated them, dropped them from a helicopter and run a tank over them. They remain invulnerable. The Doctor suggests that the cubes arrived in plain sight and may want to be observed so he suggests observing them.
The Doctor waits for four days but, when the cubes remain inert, he gets bored. He spends a frantic period of hyper-activity vacuuming the carpet, painting a fence, fixing the car and so on. When he finds that only one hour has passed he re-enters the TARDIS, only to find Rory's dad still in there, where the Doctor left him, watching the cubes. He puts Brian in charge of watching the cubes for him while he goes off in the TARDIS. He says he will stay in touch via the news feeds from Earth and offers Amy and Rory the chance to come with him but they decline.
October comes. Amy agrees to be her friend's bridesmaid. Rory agrees to go full time at work. Later, they discuss this and admit how much they like the idea of normal life. Meanwhile, Brian is keeping a video diary of the cubes. 67 days in and the cube remains inactive.
December: unknown to the world, a little girl at the hospital where Rory is a nurse, has one of the black cubes, which glows with an eerie blue light. It seems to control two medics with bizarre facial disfigurements. They are kidnapping patients.
Summer returns. Amy and Rory are celebrating their anniversary with a barbecue. Nine months have passed since the cubes arrived. The Doctor arrives during that time and takes Amy and Rory to 26th June 1890 and the Savoy Hotel in Paris. He wishes them a happy anniversary and promises them there will be no complications. He is soon apologising for the Zygon ship that was under the hotel and the fact that half the staff were alien imposters. Their next trip takes them to Henry VIII's court. They end up hiding under a bed after Amy mistakenly marries the king.
The Doctor returns them to their own time. Brian realises that they have been gone (they are only away from the barbecue for a few minutes) because they have returned in different clothes. The Doctor admits that they were gone for seven weeks because he got sidetracked. Brian asks the Doctor what happened to his other companions and the Doctor admits that some leave, some are left behind and some die. He promises that this will not happen to Amy and Rory.
Later that night, the Doctor asks if he can stay with Amy and Rory to keep an eye on the cubes. She says that she thought he would get bored but he says that he will be better at it this time. Hesitantly, he tells her that he misses her. She smiles.
Brian finishes his log for day 361 and drops off to sleep. As he does so, the cube spins around. One in the bathroom spikes Amy and takes her pulse. Another one opens in front of Rory and a fourth interrupts the Doctor's game of tennis on the Wii by firing laser bolts at him before it starts to surf the internet.
Rory is summoned to the hospital to help with an inrush of patients who have been attacked by the cubes. He takes Brian with him. The Doctor heads off to a secret UNIT base beneath the tower of London after Kat sends a message to his psychic paper. He takes Amy with him. There, they find that the cubes are all behaving individually: some create mood swings; one plays the "Birdie Song"; others have breached national security around the world. After 47 minutes, the cubes stop.
The Doctor and Amy go to get some fresh air outside. He tells her that he knows she and Rory are planning an end to their travels with him. He tells her that he keeps coming back to her because hers was the first face his incarnation saw. He wants to be with her before she fades away from him. Amy asks him not to be nice to her but he tells her that she always gets what she wants. It dawns on him that the cubes, too, have got what they wanted.
He returns to Kate and tells her that the cubes have scanned the whole planet and its inhabitants. They now have enough knowledge to attack. The best defence is to warn everyone to keep away from the cubes. Suddenly, the cubes all begin to show a blue number seven on their sides. The seven becomes a six. As the warnings are broadcast, the countdown continues.
In the hospital, Brian is snatched by the two disfigured men and wheeled away on a trolley. Rory sees them and chases down a long corridor into an elevator. The elevator is empty but one wall is a portal through to a spaceship above the Earth. As Rory steps through he sees a number of people unconscious on beds.
The Doctor enters a sealed booth to talk to a cube. It reaches zero in its countdown and then opens: inside, it is empty. Screens in the control room show CCTV pictures from around the world. People are receiving massive electrical shocks from the cubes and having heart attacks. The Doctor, too, receives a shock and one of his hearts stops. A scan he set running earlier reveals seven sites around the world where signals are originating, controlling the cubes. He recognises that these are being controlled from space via wormholes. The nearest is the hospital where Rory works.
The Doctor arrives in the hospital and notices that the little girl with the cube is giving off strange signals. He recognises her as an outlier droid. He disables her but before he can go on he begins to collapse. Amy uses a defibrillator to restart his other heart and the two find the wormhole portal in the lift. With a smile, they step through onto the space ship.
Seeing Rory and Brian unconscious, the Doctor and Amy revive them. Rory and Amy wheel Brian back through the portal and then rejoin the Doctor. He is confronting a member of the Shakri, a race of people the Doctor thought were a myth. According to Gallifreyan legend, they serve the Tally, as 'pest controllers' of the universe. The Shakri says that he has come to erase humanity before they spread like a contagion out into the stars. The Doctor argues that humanity is full of ingenuity and hope.
The Shakri vanishes: he was only the ship's interface. The Doctor uses his sonic screwdriver to use the cubes to restart the hearts of all those who 'died'. The energy released destroys the seven wormholes and the three of them leap through the portal just in time.
Back at the Ponds' house, after a celebration dinner, the Doctor makes ready to leave, saying that he knows the others cannot go with them. Brian says that Amy and Rory want to (must) go with him. The Doctor invites Brian, too, but he says that somebody must stay to water the plants. The Doctor and his friends enter the TARDIS, wave and leave.