London, 2012. In a quiet suburb on an average street, children play and construction work goes on... though an old woman named Maeve seems to know that there are connections between a rash of recent disappearances on the block. Nobody will listen to her, but another boy disappears while playing football, without a passing thought. And in the meanwhile, alone in her room, a little girl named Chloe draws another picture, this one of the missing boy, which takes on a life of its own...
The Doctor and Rose arrive in the neighborhood as preparations continue for the Summer Olympic Games, which are soon to be held in London. Rose is concerned about the number of bills posted about the missing children in the neighborhood, which leads them to begin an investigation. Rose notices that cars mysteriously stop in a part of the street, as Kel, a street construction worker, tells her, while the Doctor feels an uncertain amount of energy in the places the children disappeared. The two meet the neighbors, including Trish, the mother of the little girl that peers at them through her second-storey window. The Doctor believes Maeve's story and continues his pursuit of the truth, and Rose watches as a cat disappears right from under her nose.
Inside the house, Trish attempts to get through the Chloe, who's absorbed by her continued drawings all over her bedroom. Rose is attacked by some sort of creature in a garage - a creature made of graphite, the same material used in pencils. More interestingly, the Doctor notices he can erase the creature with a standard pencil eraser, realizing that whatever created the "squiggle creature" as he calls it just drew it into existence... some sort of child's drawing. The two end up at Trish's house, after remembering Chloe's interest from her window. Trish realizes the Doctor can help her, so she invites him and Rose in, telling them about her daughter, a lonely little girl who sits in her room all day and draws. The Doctor detects something unusual coming from Chloe, while Rose snoops around and discovers there's something lurking in Chloe's closet. In fact, it's a drawing of Chloe's father, an alcoholic who mistreated the two of them. The Doctor puts the pieces together - Chloe can manipulate reality by drawing, trapping people in her sketches or, in the case of the closet, recreating things from fantasy.
The Doctor makes contact with a being inside Chloe - a wayward Isolus, part of a gestalt mind that was accidentally left behind on Earth. The Isolus doesn't mean any harm; it's lonely, having spent an eternity with millions of its brothers and sisters, and believes the drawings that trapped the children are bringing new friends for it to play with. The Doctor and Rose return to the TARDIS, where he attempts to create a device that will allow the Isolus to free itself and be reunited with its traveling pod. Unfortunately, the Isolus believes the Doctor has hostile intentions, and so Chloe traps him and the TARDIS inside a drawing!
Remembering that the Isolus crashed in the neighborhood and its pod radiates heat, Rose determines that the pod is stuck in the asphalt on the street (hence the cars coming to a standstill). She digs it up, to Kel's dismay, out of one of the newly filled potholes. The Isolus, which has already stolen the population of the Olympic stadium waiting for the arrival of the torch, prepares one last drawing - a picture of the Earth, which will trap the entirety of humanity within a drawing. Outside, the Olympic torch comes down Trish and Chloe's street, and Rose, realizing the Isolus pod needs a heat source, throws it at the torch; ignited by the torch's heat, the pod reactivates and summons the Isolus, so the two can be rejoined and leave Earth. The Isolus leaves Chloe, who is reunited with her mother, but also frees the terrible image of Chloe's father from the closet - until it is banished when Trish and Chloe sing together, ridding the bad feelings and making the beast lose its form.
Everyone is returned from the drawings back to the way they were... except the Doctor. But he's alive, and grabs the Olympic torch and carries it into the stadium to light the flame. The Isolus leaves Earth and the Doctor can feel the love from the audience. Back on the street, as everyone watches the fireworks overhead, celebrating London's Olympic spirit, the Doctor realizes that there is something terrible coming... a storm is approaching...
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