Coal Hill Schoolteachers Barbara Wright and Ian Chesteron have the same problem student; Susan Foreman, a strange teenage girl who seems to be incredibly advanced in some areas, hopelessly ignorant in others, and overall an otherworldly presence in their classroom.
Consumed by curiosity and concern for the girl, they visit her home address and are astounded when it turns out be a junkyard. Following Susan inside, they find what they assume to be an abandoned police box and encounter Susan's guardian, her grandfather. The old man is rude and secretive and dismissive of the two teachers, which only increase their suspicions. When Ian and Barbara hear Susan's voice from inside the police box, they force their way inside.
To their amazement, the police box is much larger on the inside than it appears, and the teachers find themselves in a huge, highly advanced control room. Susan and her grandfather, known as the Doctor, are aliens who travel through time and space in this ship, which is called the TARDIS. The Doctor, fearing that Ian and Barbara will reveal their presence in this time, sets the ship in motion, taking them all to a desolate freezing wasteland in Paleolithic times. There they become involved with a tribe of prehistoric humans who are in the midst of a power struggle over who has the knowledge to make fire. With their lives under threat, the travellers narrowly make it back to the TARDIS and escape.
Setting off again, it is now all too clear to Ian and Barbara that the Doctor does not have full control over their travels, and returning to their own time may take far longer than they thought. The ship next materializes in a strange forest, and as the crew set outside to explore, the radiation meter on the TARDIS console begins to register "Danger."