NOTE: This spoiler was submitted by Mark
The movie is set in the 1860s as Amelia Rennes (Felicity Jones) travels in a horse-drawn carriage to an unknown destination. As she travels, she has a sudden panic attack and leaves the carriage. Her sister Antonia (Phoebe Fox) tries to talk her out of the venture she is about to embark on. Amelia refuses, as a young boy runs past. He is seen heading to a large venue where a hot air balloon is about to take flight. It turns out this is where Amelia was heading. At the balloon, James Glaisher (Eddie Raymayne) waits impatiently as it nears the time he is due to take off. Eventually, Amelia (who is to be the balloon’s pilot as James will be taking scientific readings) arrives in a grand spectacle, putting on a show for the crowd much to the reserved Glaisher’s chagrin. Amelia even insists on bringing Posey, her Jack Russell terrier, along with them despite James trying to put his foot down. Although Amelia is unsettled to see a vision of her late husband Piers (Vincent Perez), she keeps up the brave front and the balloon launches. Amelia then climbs above the ropes and asks James to pass her Posey, and when he does, she shocks him and the crowd by throwing the dog over the side. Thankfully, Posey is wearing a parachute and lands none the worse for wear.
In a flashback (which pepper the film), James appears before the Royal Society and explains his theory that the weather can be predicted. His ideas are seen as absurd, and he is laughed out of the building, the jeers led by Charles Green (Thomas Arnold). Returning home, he speaks to his mother (Anne Reid) and father (Tom Courtenay), who try to persuade him to pursue another avenue of science.
On the ground, James’ assistant John Trew (Himesh Patel), who is envious of James’ trip, is approached by the boy from earlier who asks to use his telescope. John eventually agrees and is surprised when the boy manages to spot the balloon through it. On the balloon, James and Amelia start rising through the cloud layer. Both delight in the unique experience, but soon run into a violent storm which sends the balloon spinning as the two attempt to make it through the rough weather.
Sometime following the death of her husband, Amelia is moping when Antonia persuades her to attend a society function. There, she is approached by James for the first time, who claims that he is attending with a friend who wishes to court a wealthy woman attending. Amelia is very put off by his quirky nature, but dances with him to put off a suitor who wishes to approach. As the two dance, James asks her if she would be willing to loan him her balloon and be his pilot while he attempts to prove his theories. Amelia realizes that James is not there with a friend but attended simply to meet her. She is angry but is persuaded by him to agree. Days later, as she starts putting the balloon together, Amelia is confronted by Antonia, who requests that her sister give up on being an aeronaut and try a much more conventional career path.
After some very close brushes with death, which includes James suffering a head injury, the two manage to make it through the storm and continue rising, with James releasing a pigeon carrying a message for Green stating how high he has made it. Eventually, the balloon manages to make it above 26,000, beating the record for the highest altitude achieved by a human.
As time passes, James and Amelia start getting to know each other better and start enjoying each other’s company a lot more with James becoming less concerned with scientific readings and starting to enjoy the experience from a personal point of view (while also releasing another pidgeon). The two also discover an air current which is home to a flock of butterflies, which confirms one of John’s theories, which James had always refuted. Amelia, however, refuses to discuss the death of Pierre.
In a far earlier flashback, it turns out that when Amelia and Pierre were on a balloon flight, something went wrong, and they needed to lose weight quickly. Having thrown everything else overboard, Pierre then sacrificed himself to save his wife by throwing himself over the side to his death.
James releases the third pidgeon; however, he finds the fourth and final one has frozen to death. As he dumps it overboard anyway (to decrease the weight), Amelia finds out James didn’t bring any clothing suitable for coping with the rapidly decreasing temperature and decides to start descending. However, James refuses, and the two have an argument over the right course of action. Eventually, Amelia agrees to keep rising, but under the condition that he accepts, they’ll have to start descending soon.
As James practices for the flight, Amelia approaches him and tells him she’s changed her mind. He is horrified, as money has already been spent preparing for it, but she is unmoved and leaves. James goes to tell his father, who now is suffering from dementia, but when his father speaks of his pride in James, it causes him to back out. Desperate, James approaches Green asking to accompany him on a flight. Green refuses and basically laughs in James’ face. John goes to see Amelia and speaks up for James, showing her a book containing his findings when studying snowflakes and tells her how much the flight means to James. Amelia goes to Pierre’s grave to talk to him about it. When it begins snowing, she decides to go with James after all.
The temperature is now below freezing, and Amelia demands that the balloon starts descending. James is now going slightly mad from the cold and insists they continue, and begins throwing equipment and sandbags overboard to speed up their ascent. The two get into a scuffle, and James earns himself a slap from Amelia when he invokes James’ name. This brings him to his senses, and he agrees that they need to start descending.
Unfortunately, it is easier said than done, as the air release valve on top of the balloon is frozen. As James falls unconscious, Amelia has no choice but to climb on the outside of the balloon and open it from the outside. However, this is hampered by the fact she is now suffering severe frostbite in one of her hands. Despite everything, she makes it to the top and manages to kick open the air release slightly, and the balloon begins slowly descending. However, Amelia loses consciousness and starts falling over the side.
When Amelia wakes up, she is hanging upside down over the side by a rope she’d tied to herself. Quicky gaining her bearings, she manages to swing back to the balloon and tries desperately to wake James up. It seems for a few seconds he has died until finally he comes too and they start to enjoy the descent.
Snow starts falling around them, however, when the snow starts to hover in front of them, they realize they’re not descending as quickly as they should be, and the balloon has started to collapse. They manage to get the air release opened fully, causing Amelia’s shoe over the side, making James realize she climbed over the balloon to save his life. This still isn’t enough to get the balloon down fast enough, so they start throwing everything over the side (James makes sure to pocket his records). When this also doesn’t work, the two resort to climbing onto the framework and releasing the basket. They then decide to use the balloon as a parachute, which slows down their descent but not completely. The two hit trees as they near the ground and James disappears while Amelia hits the ground hard and is dragged several feet before stopping.
Amelia wakes up and starts calling for James, who staggers towards her. Both are severely injured, but euphoric that they managed to survive. Battered but unbeaten, the two help each other to their feet and stumble towards help. A voice-over by Amelia states that James’ findings eventually paved the way for the first weather reports. James gives another speech to the Royal Society, and he and his field are finally accepted, with James earning huge applause from his fellows. The film ends with James and Amelia going on another balloon flight together.