The TARDIS materialises on Earth in time for the 2012 Olympic Games in London neatly between two shipping containers. The Doctor has to attempt the landing again as the first attempt has the TARDIS doors blocked by one of the containers.
The Doctor and Roses enthusiasm is soon dampened when they walk by a housing estate and see notices of children disappearing. The Doctor also notices that it is quite cold. Rose wonders what kind of a person would take children, but the Doctor is already running up a street, asking why Rose is assuming it is a person.
Going to the front lawn of one of the victims the Doctor can feel residual energy, and is confronted by the victim's father. More residents appear, and the Doctor assumes the identity of a police officer using his psychic paper. Tensions are high, and the residents are blaming anyone and everyone - including a council worker who is repairing the road for a second time. Strange things have been happening - including a dead area where cars stop working. From a window a young girl - Chloe Webber - watches the crowd.
Whilst 'investigating' Rose sees a cat that runs into a box. When she looks in the box it is empty, and the Doctor feels the energy again. Chloe has been busy drawing - and whatever she draws is taken from reality into a virtual world. She drew Dale Hicks, and when he became unhappy she also drew the cat. When she made a mistake the scribbled over it.
In a garage Rose hears a noise and goes to investigate. Knowing she shouldn't open someone else's garage she can't resist, and is attacked by a weird object. The Doctor stops it and takes it to the TARDIS for analysis: it is graphite, and Rose names it a scribble creature, and mentions the child to the Doctor.
They both visit Chloe's house and get to see Chloe's drawings. Her Mum is terrified, but cannot talk to anyone about it. As well as living creatures becoming drawings, drawing can become living things. In her cupboard is her dead father which Chloe has brought back as a monster. Putting the Chloe in a trance the Doctor is able to talk to what is controlling her, and it reveals itself as a young Isolas - a creature that travels for thousands of years a child. It usually travels with its 4,000,000,000 siblings, but has become separated, and hates being lonely, which is why it has been taking children.
The Doctor knows that the Isolas will not stop until it has more friends, and he and Rose return to the TARDIS where the Doctor constructs a device that will help. On leaving the TARDIS there is a crash. The device has smashed on the floor when the Doctor and the TARDIS disappear. Rose rushes back to Chloe's house to find she has drawn the Doctor, and refuses to return him.
Things get worse as Chloe sees the stadium for the Olympic Games filled with people, and draws trhe stadium, taking all the visitors. This is not enough, and looking through an atlas Chloe starts to draw the world.
Rose realises the Isolas pod must be outside. It is attracted to heat, and she realises that when it arrived the nearest heat source would have been the fresh tar in the road, and she digs up the road to get to the pod. But heat is not enough to reactivate the pod. Looking at Chloe's drawing she sees the picture has changed. The Doctor is now pointing at the Olympic flame. Commentary on the laptop covering the games says the flame is also a beacon of love. The flame is due to go past the end of the street, and Rose throws the pod into the flame.
The pod is reactivated, and the Isolas spore leaves Chloe to return to the pod and return to its siblings. All the missing people are returned. All but the Doctor. Rose looks anxiously for him. The commentary for the games is looking at the flame bearer who stumbles. But the flame is picked up and carried by the Doctor.
