When a gate to another world suddenly opens on Earth, Mikado City is invaded by strange creatures known as "Neighbors," malicious beings impervious to traditional weaponry. In response to their arrival, an organization called the Border Defense Agency has been established to combat the Neighbor menace through special weapons called "Triggers." Even though several years have passed after the gate first opened, Neighbors are still a threat and members of Border remain on guard to ensure the safety of the planet. Despite this delicate situation, members-in-training, such as Osamu Mikumo, are not permitted to use their Triggers outside of headquarters. But when the mysterious new student in his class is dragged into a forbidden area by bullies, they are attacked by Neighbors, and Osamu has no choice but to do what he believes is right. Much to his surprise, however, the transfer student Yuuma Kuga makes short work of the aliens, revealing that he is a humanoid Neighbor in disguise. [Written by MAL Rewrite]

The story follows a boy named Quon and others who suddenly wake up with supernatural powers.

Hikari Hanazono has always been able to do things that normal people cannot. As a child, she assumed no one could beat her—until she met Kei Takishima. Thinking she would win, Hikari challenged him to a match. But things didn’t go as planned; she lost not once but each time she rechallenged him. From that point on, she has sworn to best Kei at everything, ranging from academics to athletics. To achieve her goal, Hikari enrolls in the same school as Kei—Hakusenkan, a prestigious institute for the wealthy. As a pair, they hold the top two rankings in school and are among seven of the academy's best students in a class known as Special A. While Hikari treats Kei as a rival, she is completely oblivious that he harbors hidden feelings for her. Together, the members of Special A deal with competition, friendship, and just a bit of love. [Written by MAL Rewrite]

Sakurai Tomoki has settled into his life with the two angeloids, Ikaros and Nymph, and is enjoying himself immensely. However, he keeps having weird dreams and asks all of his friends to help him investigate the cause. Nymph conjures up a device that enables people, but not angeloids, to enter other people's dreams. The device malfunctions at first but eventually they get to what was supposed to be Tomoki's dream but discover that something is very wrong with it. Later, a meteor comes crashing down from the skies at the site of the large cherry blossom tree where Tomoki first discovered Ikaros. An extremely well endowed blonde angeloid with a huge sword emerges from the meteor and sets off in search of Tomoki!