In 1963, while attending a party, astrophysics student Stephen Hawking meets Jane Wilde, a fellow student at Cambridge University who is studying literature. Both are working for their PhDs. The two bond during the night, and Jane gives Stephen her phone number.
Although Stephen excels at mathematics and physics, his friends and professor are concerned over the lack of a topic for his thesis. Stephen does not focus on this, instead he concentrates on his relationship with Jane, and they attend a ball together. Stephen and his professor go to a lecture on black holes, where Stephen first notices he is not able to walk very quickly. Stephen begins to wonder about black holes, and speculates that they may have been a part of the creation of the universe.
Stephen tells Jane his theory, and that he wishes to wind back the clock to the beginning of the universe to see what happened. While pursuing his research, Stephen's muscles begin to give out while walking. Visiting the hospital, the doctor tells him that he has motor neuron disease, and that although his brain will remain unchanged, his muscles will soon be uncontrollable, unable to walk, talk, or move most of his body. He is told that he has approximately two years to live.
Becoming reclusive, Jane and Stephen's roommate, Brian, attempt to get Stephen out of his room, Jane tells Stephen that she loves him. Jane talks with Stephen's parents, who explain the full situation to her, Jane says that she will stick by Stephen. Cheered up by Jane and his friends, Stephen tells his professor that his thesis paper will be about time. When asked ‘what about time?’, Stephen merely responds ‘time’.
Soon after, Stephen and Jane marry and soon have a son. Stephen's ability to talk has become progressively worse due to the motor neuron disease. When he finally presents his thesis to the examination board that a black hole was responsible for the creation of the universe, they tell him, although there are some errors, his theory is revolutionary, and he is awarded his doctorate. However, while celebrating with Jane and his friends, Stephen realises he is now unable to walk, and he becomes dependent on a wheelchair.
After having a second child, a daughter, Stephen has a theory about the visibility of black holes. He presents his theory at a lecture where the professors are astounded that Stephen has discovered what none of them had been able to. This leads to Stephen beginning to become a world-renowned physicist, which he and Brian celebrate that night.
Stephen soon gets an electric wheel chair, allowing him to move around with the limited hand function he has left, and begins to play with his children again. However, while focusing on her kids, Stephen's health, and his increasing fame, Jane is unable to get work done on her own thesis paper, leading to her frustration.
After visiting his parents, Jane tells Stephen about her spiraling depression, and he says he understands if she needs help. At the suggestion of her mother, she joins the church choir, where she meets a handsome conductor named Jonathan. She and Jonathan become close friends, and she employs him as a piano teacher for her son. Jane, Jonathan, and Stephen soon have dinner together, Stephen and Jonathan becoming friends as well.
He soon becomes a friend of the entire family, helping Stephen with his illness, supporting Jane, and playing with the children. Soon afterwards, Jane becomes pregnant with a third child. After giving birth, they once again visit Stephen's parents, bringing Brian and Jonathan along. Stephen's parents see how Jonathan gets along so well with the Hawkings, and ask Jane if the baby is his.
Jane is appalled that they would think so, but sees that Jonathan overheard the conversation. Jane tries to stop him from leaving, and while the two are alone outside, Jonathan admits that he has feelings for her. Jane admits she has feelings for him as well. Jonathan then stays away from the family for a while, but Stephen visits him, saying that Jane needs him.
With his fame increasing, Stephen is invited to a concert in Bordeaux. While he is attending, Jane and Jonathan take the children camping. However, while in France, Stephen contracts pneumonia, Jane quickly visits the hospital. The doctors tell Jane that the only way to save him is with a tracheotomy, which will render Stephen speechless. She tells them to operate anyway.
Stephen becomes depressed soon afterwards, along with Jane who says goodbye to Jonathan for what she believes is the final time. Hiring a nurse, Elaine, Stephen begins to use a spelling board, and uses it to communicate with the nurse. The two get along well, and Stephen soon buys a computer with a voice synthesizer built in, which responds to clicks from Stephen, he is able to use it to speak at an almost normal pace again.
Stephen uses this to write a book, A Brief History of Time, which becomes an international best-seller. One day however, Stephen tells Jane that he has been invited to America to accept an award, and he will be taking Elaine with him. Jane is upset that Stephen has not told her, and this becomes the trigger for Jane and Stephen’s realisation they can no longer remain married to each other.
Stephen goes to a lecture with Elaine, the two having fallen in love. At the same time Jane goes to see Jonathan, the two reuniting as well. While at his lecture in America, where he is introduced by his old professor, Stephen sees a student in the front of the room drop a pen off of her desk. Stephen imagines himself getting up to return it, almost crying at the reminder of how his disease has affected him.
However, he presses on, and gives a inspiring speech about human endeavour, the audience giving him a standing ovation. Soon after, while Jane and Jonathan are living together, Jane receives a letter from Stephen inviting her meet the Queen with him. Jane and Stephen reunite as they meet her, the two happily talking in the courtyard. Stephen and Jane look out to see their children playing, Stephen joyfully typing "look what we made."
In a final scene, the film rewinds to the moment Stephen and Jane first met, mirroring Stephen's wish that he would like to reverse time itself to see what happened at the beginning of the universe. The closing text states that Jane and Jonathan later married, and that Jane and Stephen remain close friends to this day.