Yū Otosaka is a boy who one day awakens the ability to temporarily possess anyone in his line of sight. Using this power to peer at other students' answers during exams, Yū manages to enter a prestigious school, where he once again uses his ability to woo the school's madonna, Yumi Shirayanagi. However, Yū's perfect scores catch the attention of the student council president, who challenges him to take the exam again or else face expulsion on grounds of cheating. This turns out to be a trap set up by a girl named Nao Tomori, who had been observing his abilities in action. Yū attempts to flee but is caught by Jōjirō Takajō, who can move at uncontrollably high speeds. With her target captured, Nao, who can make herself invisible to a specific target, arranges for Yū and his little sister Ayumi to be transferred to Hoshinoumi Academy, a school for those with abilities like his. Getting dumped by Yumi as a result of the restrictions forced upon him, Yū reluctantly prepares for his new life as a member of Hoshonoumi Academy's student council.

Yū begins his life as a member of Hoshinoumi Academy's Student Council, whose job is to ensure the safety of students with supernatural powers. Their first job leads them to Nanba High School, where they catch a student named Udoh using his ability to produce x-ray photos of girls in their underwear, selling them for a profit. The next day, Nao takes Yū to see her big brother, who had been experimented on for his ability to manipulate sound waves, leaving him emotionally destroyed. Nao further explains that thanks to a person she trusts, she was able to escape the school that experimented on her brother and bring him to a friendly environment.

After Yuu eats lunch with Jojiro at the cafeteria, their second job leads them to a user with two abilities, after investigating the narrow area, they found out that it was the popular singing idol and vocalist of How-Low-Hello Yusa Nishimori, who's being chased by Someone. after fighting the person chasing her, a guy named Sho leads them back to a club where Yusa is in hiding, she has the ability to allow a dead person possess her body. and the dead person possessing her is her older sister Misa, who has the ability pyrokinesis. the reason Yusa was being chased was she accidentally brought home a smartphone of a TV Producer that has messages and stuff that will arrest him if taken by the cops. with Nao making a threatening plan for the TV Producer, that night Yusa confronted the TV Producer and turned to Misa threatening him and returning the smartphone back to him. after that Nao offered Misa that she will arrange Yusa for her to transfer to Hoshinoumi Academy, after she agrees Sho confessed her feelings for Misa and told him and Kota to live their own life and thanks them for everything.

After Yusa's loud transfer to Yuu's class, Nao brings her and the others to their third job in Kannai Academy, where they believe a user with telekinesis is attending. As proof, Nao shows them footage of a baseball pitcher, Arifumi Fukuyama, who pitches a knuckleball. However, Nao observes that Arifumi was about to throw a straight ball, but used his ability to position the ball and make it a knuckleball. After confronting Arifumi, who refuses to stop using his ability, Nao holds a baseball match between Kannai and Hoshinoumi's teams, saying that if they win, Arifumi will stop using his ability. After eight innings, both teams are evenly matched. In the last inning, Misa runs from second base to home with the help of Nao and Hoshinoumi subsequently wins by two to one. As a result, Arifumi agrees to stop using his ability, and Yuu possesses him for a little experiment by Nao.

Learning of a user with the ability to fly, the student council camp out in the mountains where the user has been training to control his ability. During the first two nights, Yusa tells the other members about her relationship with Misa, while Yuu interacts with Nao, talking with her about the band Zhiend and her dream of filming them. He then talks to Jōjirō about their abilities and how long they will last. The day after, the ability user confronts the council members and tries threatening them into leaving, but Nao dismisses his threat as a bluff. The ability user then steals Nao's camcorder from her and attempts to escape using his power, but is stopped by Yuu's ability. After Nao convinces the user to stop using his ability, Yuu returns to his condo to find Ayumi sick with a cold.

While Ayumi stays at home to recover from her fever, Yuu and the others learn that a student with a "collapse" ability is in the condo. As a result, Nao suspects Ayumi of being the ability user, believing she might be developing an ability of her own. As Yuu, Nao, and Yusa check up on her, Ayumi describes a dream she had about the ground suddenly cracking, prompting Nao to suggest that everyone be cautious around her. The next day, as Ayumi's temperature goes down, Yuu advises her to stay at home so she can be safe, but she decides to sneak out and go to school anyway. There, she is confronted by her classmate, Konishi, who accuses her of stealing the boy she liked away from her, then comes at her with a cutter. Pushed into a corner, Ayumi suddenly activates her ability, causing the school building to collapse with her still inside. As Yuu desperately searches through the wreckage for any signs of Ayumi, a piece of rubble falls towards him. Afterwards, Kumagami is shown standing over the wreckage.

After the school collapse, Yuu wakes up in a hospital bed and is informed that Ayumi died. He subsequently enters shock and locks himself away in his apartment, becoming a recluse. Later on, Yumi comes by to talk to him but is turned away. Yuu ends up running away to another city and attempts to survive on snack foods while passing the time at a local arcade. However, as he grows progressively more unstable, he begins using his powers to pick fights with gangs. Before he can turn his attention to drugs, Yuu is stopped by Nao, who had been observing him the entire time using her invisibility. Nao attempts to reconnect with Yuu by taking him to Jōjirō's house and offering him some omurice. Upon eating it, Yuu realizes it tastes exactly like the dish that Ayumi would make for him using the secret pizza sauce. He soon resolves to return to the student council with Nao to work hard in memory of his sister.

After Yuu returns to school, Nao assembles the student council together to watch Yusa's new video before inviting Yuu to go a Zhiend concert with her. After the concert, Yuu comes across Zhiend's blind vocalist, Sara Shane (or Sala Shane), who treats him to dinner and hears about his recent loss. Believing it might help Kazuki, Yuu decides to take Sara to meet him, hearing from her about the troubles she faced in her career before she went blind. When they arrive, Sara uses her song Fallin to calm Kazuki down from his rage, allowing him to recognize others once again. After seeing Sara off, Yuu is thanked by Nao for improving Kazuki's condition. She then becomes curious as to why he feels so nostalgic over Zhiend's music.

While attending the Zhiend concert with Nao, Yuu feels a familiar sensation upon hearing what is supposed to be a brand new song, suddenly causing him to have a sudden flashback. In these memories, Yuu and Ayumu are living together in a facility, where they are monitored for their abilities. When Ayumi's collapse ability caused damage to the facility, a researcher helped Yuu escape and use his true ability, "plunder", to borrow the abilities of other users and reach his brother, Shunsuke, who uses a time-leap ability to change the world. After Yuu regains consciousness in the present, aware that he has a brother, he and Nao are approached by Kumagami, who takes them to a hidden facility to meet with Shunsuke and hear his story.

Shunsuke explains what happened after time-leaping into the past three years. After explaining his situation to Kumagami and joining up with his allies, Shunsuke began trying to think of a way to keep them safe from the facility. As Shunsuke time-leaped multiple times in order to find an answer, his vision growing weaker with each leap, he eventually came upon the idea to found a school specifically for ability users. Following his final leap, which left him blind and thus unable to use his ability further, Shunsuke managed to buy out an educational facility before arranging for Yuu and Ayumi to have their memories of him erased so he can work behind the scenes. After Shunsuke finishes explanation, Yuu loots his time-leap ability and returns to the day before Ayumi died. Informing Nao of the situation, Yuu takes Ayumi's collapse ability away from her, before she and Nao use their abilities scare off Konishi so she can't bring harm to Ayumi. With Ayumi finally safe, she and Yuu regroup with Kumagami, who takes them to see Shunsuke.

After being filled in on the situation, Shunsuke urges Yuu to stay with Ayumi at his research facility until his abilities disappear, as they put him at risk of being targeted. There, he learns that special abilities are the result of inhaling particles spread by a short-period comet called Charlotte. Later, Kumagami's aide Furuki is threatened into handing him over to a terrorist group, who force him into telling them everything he knows about ability users. Using this information, the terrorists kidnap Nao and hold her, Kumagami, and Furuki's family hostage in exchange for Yuu. Learning of this, Yuu goes to rescue them. Upon meeting up with the terrorists and ensuring the safety of Furuki's family, Yuu is attacked by another ability user, who slashes his eye, preventing him from time traveling. The pain of the wound triggers his collapse ability, which destroys the building. Although Yuu uses his telekinesis to protect himself and the other ability user, Kumagami is impaled after protecting Nao from the wreckage and dies as a result, devastating Shunsuke.

Two days after the incident, Yuu wakes up in the hospital and learns of Kumagami's death. As Yuu's friends come to visit him during his rehabilitation, he has a discussion with Misa about life and death, encouraging her to visit her parents while she still has a chance. She gets this opportunity when Yusa hosts a food report on their parents' restaurant, allowing Misa to express her appreciation to them, which in turn gives Yuu a better appreciation of Ayumi's cooking. Later, as Yuu becomes determined to help Shunsuke, who is still in turmoil over Kumagami's death, Nao suggests that he could protect all of the ability users around the world by simply stealing their abilities. Despite the risk of taking on so many powers, Yuu accepts and then confesses his feelings to Nao, who tells him she will be waiting until he succeeds, before taking her ability. After informing Shunsuke of his mission, Yuu prepares to go overseas to find someone with a power similar to Kumagami's to track down other ability users. He takes the abilities of Jōjirō, Yusa, and Misa, the latter of whom leaves behind a letter for Yusa expressing how much fun she had. Before Yuu leaves, Nao hands him some flash cards while he gives back her MP3 player as a vow that he will come back from his journey alive.

Beginning his journey in South Africa, Yuu manages to find an ability for seeking out other users and slowly starts looting abilities from each esper he meets, earning him a reputation as the One-Eyed Grim Reaper. Later, whilst infiltrating a facility using ability users as soldiers, he further gains the ability to detect those who haven't awakened their abilities yet, using an illness power to force them to awaken so he can loot them. As his journey continues across many other countries, the burden of taking on so many abilities start to take their toll on Yuu as he struggles to keep them under control, soon becoming afraid of what he might do unconsciously while sleeping. He soon starts losing his memories and sense of self under the stress on his brain, the only thing tying him to his humanity being the flash cards Nao gave him. Ending his journey in Beijing, Yuu is attacked by a man with a crossbow, receiving heavy injuries before taking the final user's ability and being recovered by Shunsuke. Awakening at hospital back in Japan, Yuu is left with no memories of who Nao is, but she is nonetheless grateful that he kept hold of his flash cards all this time. With no abilities to cause them worry, Yuu, Nao, and the others look forward to the memories they'll make from now on.