Amy and Rory have tried to adjust to normal life without travelling with the Doctor. One day billions of small black cubes appear around the globe, but they appear to be inert and invulnerable. The Doctor arrives to help, having been alerted by news stories. UNIT storms the Ponds' house soon after in response to the Doctor's arrival; the UNIT force is led by scientific adviser Kate Stewart, the daughter of the Doctor's friend and former UNIT commander, Brigadier Lethbridge-Stewart. Kate explains that they have no idea of the purpose of the cubes and hope the Doctor can help. After several days of watching the cubes without anything out of the ordinary occurring, the Doctor decides there is no problem and puts Rory's father Brian in charge of watching the cubes as he returns and departs in the TARDIS.
Over the following year, Amy and Rory live out their lives, making commitments despite not knowing if they will always be around. The Doctor visits them at their wedding anniversary party and takes them on a trip for seven weeks, though returns them a few minutes after leaving. Brian notices their absence and, in private, asks the Doctor the fate of his previous companions. The Doctor admits that while most had left on their own or were left behind, some have died, but promises that will not happen to Amy or Rory. Humanity forgets about the cubes' arrival, and use them as paperweights and similar mundane functions. Unknown to anyone at the hospital where Rory works, a young girl with a cube controls a pair of identical orderlies with distorted faces to capture a few selected patients.
A year after their arrival, the cubes start to activate, scanning the world's information networks and acting in self-defence. The Doctor realises that the cubes are part of a "slow invasion". While Rory and Brian go to the hospital to help those injured by the cubes, the Doctor and Amy are summoned to the UNIT headquarters under the Tower of London where Kate shows them several cubes under investigation, every single one behaving in a different fashion. The cubes then simultaneously display the number "7" and slowly count down. Meanwhile, at the hospital, Brian is taken by the two orderlies to a lift, where they disappear. Rory soon follows and finds that the back of the lift is a portal to a spaceship in Earth's orbit.
The cubes all open when they reach zero, appearing empty, but soon reports of people dying from cardiac arrest appear from around the globe. The Doctor finds that one of his own hearts has stopped, and realises that the cubes sent out an electrical impulse that killed about one-third of the human population. Kate's team traces a communication from the cubes to seven different outposts across the world, including one at Rory's hospital, and the Doctor and Amy race there. Amy uses a defibrillator to restart the Doctor's heart. They find the girl, who the Doctor realises is an android, and disable her before locating the lift and the portal.
Aboard the ship, Amy and Rory rescue Brian while the Doctor encounters a hologram of a member of the Shakri, who, according to Gallifreyan legend, were self-appointed "pest controllers" in the universe. The Shakri states that he and six other ships tied to the other outposts are there to wipe out humanity before it spreads across the galaxy, and prepares to launch a second wave of cubes to kill even more before disappearing. The Doctor uses the ship's computer to reverse the shock the cubes gave to the original victims, restoring them, and the three escape the ship before the feedback from the cubes causes it to explode. As the world recovers, the Doctor prepares to leave when Brian insists that Amy and Rory go with him, stating the adventures they have with him are a once-in-a-lifetime opportunity. He tells the Doctor to "just bring them back safe". The three say goodbye to Brian and depart in the TARDIS.
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