The crew of the Icarus II are sent into deep space to reignite the sun, after the failure of the first mission, Icarus I, seven years prior. It takes 16 months for them to reach close proximity to the sun, as mentioned in the introduction voice over by Robert Capa (Cillian Murphy). As the ship nears the sun, solar noise known as "the [communications] dead zone" begins to interfere with radio communications to Earth. As the ship encountered the "Dead Zone" seven days earlier than expected, the crew is now left with just 24 hours to collect all of their individual thoughts and send each of them off to their loved ones in a last message "packet".
Capa has difficulty in finding his words, and makes several different attempts at his message, accidentally "running out the clock" on fellow crew member Mace (Chris Evans). This results in a fight between Capa and Mace, which lingers as open animosity between the two, despite Mace's apology. Icarus II's captain, Kaneda (Hiroyuki Sanada) forces Mace to relax with a relaxing video. Afterwards, Mace and Capa seem to become friends again.
The ship has an oxygen garden to provide both food and carbon to oxygen recycling during the trip. It is noted that while the ship is only about 2/3rds of the way to its destination [the sun], the garden has been producing oxygen at better than expected rates - the ship already has enough oxygen stored up for the delivery, and a quarter of the return trip.
The crew Psychiatrist, Dr. Searle (Cliff Curtis) is looking out from the ship's viewport at the approaching sun one day, and is curious what it would be like to experience the unfiltered view. The ships computer (Chipo Chung's sensual voice) warns him that he can only tolerate 3.1% of the actual light, so he accepts this and sets the system for 30 seconds of viewing at this 3.1% rate. The result has some kind of effect on Searle, who begins to spend many hours in the viewing room, repeating his exposures to the sun so often that his skin eventually peels away and sores cover his face. It is never clear to the audience if Dr. Searle is possibly addicted to this exposure, possibly believing it to bring some form of enlightenment, or is perhaps trying to determine if visualizing the star was a possible reason for the demise of Icarus I's mission. Throughout the movie, you can see Searle's continuing deterioration from spending too much time looking at the sun.
While we are uncertain as to Dr. Searle's motives in staring at the impending star, we are clearly aware that the ship's Captain, Kaneda, has been researching the Icarus I's logs in an attempt to discover what went wrong, and thereby prevent his crew from making the same errors.
As the crew travels past Mercury, they unexpectedly pick up a signal from the Icarus I's distress beacon, only hearing the faint signal because it was able to bounce off the iron in Mercury's mass. Emphasizing that some of those aboard Icarus I could still be alive, Captain Kaneda explains this point to the crew, and begins a discussion as to whether the current mission should be altered in order to check on the Icarus I distress beacon. Mace is not happy with the choice to divert from their original mission, since, as he puts it, "Our mission is to deliver the payload to the nearest star, because it is dying."
Dr. Searle says that he agrees with Mace's assessment, but adds that diverting to the Icarus I could possibly add a second payload [bomb]. He argues that since the Icarus bombs have never existed before and therefore have never been actually detonated either, their existence is "entirely theoretical" and having two could be advantageous if something went wrong with the first one. There is further heated discussion, which Captain Kaneda finally stops by saying he is handing the decision to the ships most informed person in these matters, theoir physicist, Capa.
Capa is troubled by being asked to make this decision. He explains to the captain that he simply doesn't have enough information to make an informed and rational decision, and the best he can do is to "flip a coin". When Kaneda asks "So? heads or tails", Capa replies "Heads: two last best chances are better than one last best chance".
Capa's decision is finalized by the captain: Both Icarus's will rendevous togther. The ships Navigation Officer, a brilliant child prodigy named Trey (Benedict Wong), plots the course, checks it three separate times, and satisfied he has been accurate, shifts the Icarus's course to intercept the Icarus I. In the many calculations, Trey misses one - the need to readjust the heat sheild that is keeping the ship alive. This error is discovered when there is an emergency declared by the computer after slight damage to the heat sheild results from Trey's mistake.
The true extent of the damage can only be assessed, and then repaired, buy leaving the ship and working directly in space. Captain Kaneda asks for a volunteer to accompany himself, and after refusing to allow the second in command to join him, Capa is "volunteered" by Mace - this is Mace's way of stating that the current events are a direct result of Capas decision to alter the original mission, and the "volunteering is clearly made in anger and not by deciding if Capa was the best man for the job." Nevertheless, Capa accepts the implicit challenge, and Kaneda agrees to let him accompany him on the repairs spacewalk.
As Capt Kaneda and Capa exit the ship to begin repairs, the ships pilot, Cassie (Rosie Byrne), moves the Icarus's position so as to provide the two spacewalking astronauts as much "shade" she can provide. She does this knowing it will result in the loss of the two communications towers needed to return to Earth later. The tips of the comms towers burn up as they continue to revolve around the living quarters, in and out of the sunlight sparking. In consequence, Cassie unwittingly sets off another chain of events, when the still revolving and burning remnents of the communications tower causes a beam of sunlight to deflect towards the centre of the ship and onto the Oxygen Garden. This results in a fire that initially the ship copes with, but soon it flashes out of control and threatens not only the garden, but the entire ship itself.
Corazon (Michelle Yeoh) rushes to her rapidly burning garden and requests entry, thinking she can save it but Mace, weighing up the situation quickly, realizes that the mission and ship will be lost unless drastic action is taken so he orders the computer to release all the stored oxygen in the tanks, to provide such an enormous boost to the fire that it will literally "blow itself out" (this very same technique is actually used on oil platforms from time to time) however knowing too that this will have a consequence of completely destroying the garden. The order and supposition is correct on all accounts; putting out the fire and destroying the garden but most importantly the ship itself had been left relatively unscathed saving the mission.
During this event, the computer begins take automatic control of the Icarus, in order to return the heatshield back to cover the living quarters as continued exposure threatens the mission (which due to Cassie is now protecting the two astronauts from being vaporized by mere direct exposure to the sun). Cassie realizes that this manuever will result in the death of the two spacewalkers and she tries to countermand the order but the computer refuses to be ignored.
Cassie and the computer fight over control for a few moments, with Cassie eventually using an over-ride command that needs to be authorised by a second crew member. Cassie turns to Mace to have him say his authorisation code but he won't - he believes the mission far outweighs the loss of two astronauts. When Mace refuses to go along, Cassie pleas at the Communications officer, Harvey (Troy Garity). Harvey immediately issues his authorisation and Icarus begins to move back into position to safeguard the two astronauts, by providing maximum possible shadow.
Silently not agreeing, Mace directly calls Captain Kaneda and asks him to support him, countermanding the orders just issued by Carrie and Harvey - a decision that will result in his own (Captain Kaneda) death and of Capa. Kaneda agrees with Mace that the mission is more important than the lives of himself and Capa (even though, as we later learn, only Capa can fire the payload) and the captain tells the computer to resume corrective shading and proceed with the mission, which it does.
As the ship begins to lose cover for the two astronauts, Kaneda orders Capa to go back to the ship, as he patches the last of the heatshield damage by himself. Capa complies, and shortly after, Kaneda fixes the remaining damage, and then meets his demise with exposure to the sun.
Because of the loss of their oxygen garden they now have no choice but to intercept Icarus I. Trey still blames himself and is put on suicide watch.
Now alongside Icarus I, Searle, Capa, Mace, and Harvey board to discover that there is enough food to last; a flourished oxygen garden and a workable payload. However, there has been an error to the conditioning unit that will not allow the ship to move. Additionally all crew members are found burned to death in the viewing room, the result of the filter being turned off. The comment is made that if the Icarus I were not behind the shield of Icarus II, those seeing the burned crew members would suffer the same fate.
While the crew is investigating, the airlock connecting the Icarus I to the Icarus II is destroyed, as a result, we later learn, by sabotage. They find one suit that would let Capa go back (as he is the only one able to deploy the payload) to Icarus II. Searle stays to manually open the shafts while Harvey and Mace use lining of the ship to cover themselves with, so they can hold onto Capa as he is shot towards the Icarus II and thus make it in themselves. During the actual shooting, Harvey falls out into outer space and is frozen. His body can be seen being broken apart when it flies into the ship. Mace suffers frostbite but lives and rapidly recovers.
As Icarus II leaves, Searle enters Icarus I's viewing room to prepare for his death, for when Icarus II leaves, there will be no shielding from the sun. He burns to death and joins the Icarus I crew on becoming dust.
Corazon calculates how much oxygen they have and how much they need to complete the mission. She concludes there is enough for four people to live to the delivery of the payload. It is decided Mace will kill Trey but when he goes to carry out the act, he finds Trey has already appeared to have committed suicide. He returns to blame Capa for all of the deaths and again the two fight.
In the payload room, Icarus II's computer tells Capa there is not enough oxygen for them to live until they deliver the payload. He says that Corazon did the math and himself, Corazon, Mace, and Cassie should have enough to last. He claims there are four crew members but the computer says there are 5 and one is unknown. Capa learns the location of the fifth on the ship and finds it is Captain Pinbacker (Mark Strong), who has survived from Icarus I. He is terribly burnt everywhere on his body and is clearly psychopathic. Pinbacker reveals he sabotaged the first mission because it went against God. He slices a wound in Capa's chest and chases him through the ship. Pinbacker then sabotages Icarus II's computer just as he did on his own ship. [In commentary on the DVD it is said that Pinbacker also murdered Trey.]
He next finds Corazon in the remains of the oxygen garden and just as she finds a single seedling rapidly growing out of the newly burnt soil, giving her and the mission hope of not just survival but even returning to earth, Pinbacker kills her. Mace goes into the cooling unit to fix the Icarus II's mainframe by immersing himself in the coolant (liquid nitrogen?). He eventually freezes and is caught in the machine so he bleeds to death.
Capa divides the living quarters from the payload and goes into the payload to manually ignite it. There he finds Cassie hiding and is confronted by Pinbacker. He manages to ignite the payload and as the payload deploys he finds peace, accepting his death and stares into the flames of the sun as it looms ever closer.
Back on Earth, Capa's sister (Paloma Baeza) and her children (Archie and Sylvie Macdonald) are outside in a park covered with snow as she watches the last message sent to her by Capa. A brighter than usual sun is seen finally breaking through the clouds over a frozen Sydney Harbour showing they succeeded in their mission.