My Hero Academia's manga and anime are broken into Sagas and Story Arcs. The following are the Saga and Arc names, a description of the Arc's plot, and the chapters and episodes they comprise.
Note: Most Sagas and Story Arcs are fan-made or community-made names to better organize the series. They are not official names.
U.A. Beginnings Saga#
Main article: U.A. Beginnings Saga
Entrance Exam
Born without special powers in a world where 80% of the population has them, Izuku Midoriya still dreams of becoming a Hero. An unexpected encounter with the legendary Hero All Might gives him a chance to change his fate, but first he must master his newly-acquired Quirk in order to pass U.A.'s Entrance Exam.
Quirk Apprehension Test
Under the threat of expulsion on their very first day at U.A., the students of Class 1-A have their ability to properly use their Quirks judged by their strict homeroom teacher, Shota Aizawa, to determine if they are fit to be Heroes or not.
Battle Trial
After receiving their Hero Costumes, the students of Class 1-A are separated into teams of two and face each others' teams in an indoor Battle Trial, where Izuku must battle his childhood friend and rival, Katsuki Bakugo, for the first time.
U.S.J.
Class 1-A takes a trip to the Unforeseen Simulation Joint in order to hone their rescue skills. However, a group known as the League of Villains unexpectedly show up at the facility, and the students must survive their first real battle against actual Villains.
U.A. Sports Festival
The U.A. first-years participate in the U.A. Sports Festival, showcasing their abilities in different competitions in order to catch the attention of Pro Heroes. Amidst Izuku's first chance to show himself to the world, he comes to learn the details of Shoto Todoroki's past.
Vs. Hero Killer
Izuku and his classmates travel to their chosen workplaces to gain experience while training under the supervision of Pro Heroes. Meanwhile, evil begins moving about in Hosu City, eventually leading to a confrontation between three young Heroes-in-Training and the Hero Killer: Stain.
Final Exams
As the end of term approaches, Class 1-A has to face both a written test and a practical exam. However, in a surprising twist, they must face their teachers in combat in order to pass the Practical Exam, with Izuku and Katsuki forced to team up against All Might.
Forest Training Camp
U.A.'s first term has ended and Summer Break has begun. In order to hone their skills, Class 1-A goes on a school trip to a Quirk Training Camp under the supervision of the Hero Team the Wild, Wild Pussycats. Their peace doesn't last long, however, as they're soon surprised by a sudden attack from an elite squad of Villains.
Hideout Raid
The League of Villains' attack on U.A.'s Summer Training Camp has left deep scars: Katsuki has been kidnapped, and faith in the institution has been greatly shaken. In the face of this incident, Pro Heroes and the Police Force mobilize themselves for a raid on the Villains' hideout in order to rescue the kidnapped student, while the greatest evil begins to make his move.
Rise of Villains Saga#
Main article: Rise of Villains Saga
Provisional Hero License Exam
U.A. has transitioned into a boarding school; Class 1-A begin their new life living at U.A. The first task Class 1-A needs to accomplish at their new abode is finishing their training which they failed to do at the camp so that they can be ready to take on the Provisional Hero License Exam.
Shie Hassaikai
U.A.'s second semester has finally begun, and some first-years are preparing to apply for Hero Work-Studies. Izuku attempts to land a position at Sir Nighteye's office, headed by the former Sidekick of All Might. Meanwhile, a multi-office investigation involving Sir Nighteye eventually leads to the hunt of a former Yakuza member and a mysterious young girl...
Remedial Course
Having failed the Hero Provisional License Exam, Katsuki Bakugo, Shoto Todoroki, and two familiar members of Shiketsu High School take Remedial Courses, tasked with winning the hearts of the kids from Masegaki Primary School. In the meantime, Endeavor has a serious talk with All Might.
U.A. School Festival
The U.A. School Festival is approaching, and Class 1-A wants to put up a worthy performance against the public who doubt their worth. Amidst beauty pageants, wacky performances, dancing, and food, a gentleman and his partner are desperate to make their mark in history, and U.A. is their target.
Pro Hero
The biannual Hero Rankings are published, and Endeavor has taken his spot as the new Number One Hero. Torn by the invisible pillar he has to protect and his tense familial ties, Endeavor and the Number Two Hero, Hawks, discuss the rumors behind the Nomus when a sudden attack from a new Nomu puts Endeavor's role as Number One to the test.
Joint Training
Class 1-A and 1-B compete against each other in a Joint Training Battle; joining them is Hitoshi Shinso who is eager to enter the Hero Course. While the exercise is being held, Izuku discovers a new secret about One For All, one that none of the previous eight users ever could have dreamed existed.
Meta Liberation Army
All For One's personal confidants have given Tomura Shigaraki a near-impossible challenge that, if he can complete, will prove he is worthy of being his master's successor. Meanwhile, the Meta Liberation Army, a group that opposes Quirk restriction laws, has kidnapped Giran in an effort to lure the League of Villains into a trap, not wanting them to become more infamous than Destro, the leader of the original Meta Liberation Army.
Endeavor Agency
With the Hero Work-Studies back in effect, the three top students of Class 1-A study under the new Number One Pro Hero. Meanwhile, Endeavor himself undergoes an uncharacteristic epiphany.
Paranormal Liberation War
After a tip from Hawks and a new source of intel in Tartarus, the Heroes have assembled all of the information they need to confront the Paranormal Liberation Front head-on - a confrontation that will completely change the course of society as everyone knows it.
Final Act Saga#
Main article: Final Act Saga
Dark Hero
In the aftermath of the Paranormal Liberation War, and the decline of Hero Society, Izuku leaves U.A. High, working alongside All Might and the Top Pro Heroes to track down the remnants of the League of Villains, as well as continue to harness the full power of One For All in preparation for the final battle against All For One.
Star and Stripe
With Tomura Shigaraki's body nearly complete, All Might requests immediate aid from the foreign Heroes. Enter America's Number One Hero, Star and Stripe, arriving to help defeat the Villain. But "Tomura" is prepared to fight back, and do anything to accomplish All For One's next goal: stealing her Quirk, New Order.
U.A. Traitor
The pieces are in place and Class 1-A and the rest of the remaining Heroes are preparing for the final fight to take down All For One, Tomura Shigaraki, and the remnants of the League of Villains/Paranormal Liberation Front for good. However, things become complicated when the fabled "U.A. Traitor" suddenly emerges...
Final War
The time has come for the final battle between the Heroes and Villains to decide the fate of the world. All For One thinks he has the upper hand in finally cornering Izuku Midoriya and One For All, but thanks to Yuga Aoyama and the power of the Warp Gate Quirk, the Heroes turn the tables, splitting the Villains up to divide and conquer.
Epilogue
With the Paranormal Liberation Front defeated, the Heroes are slowly but surely rebuilding society. Class A is moving onto their next year, though some of its members are still dealing with the aftermath of the War.