Spoiler Warning for the My Hero Academia manga and anime series!
With no canon romantic relationships, My Hero Academia focuses on friendships that stand the test of time and even newly-kindled ones. Some of the relationships have endured great loss or even began as rivalries, while other characters were meant to be in each other's lives from the very beginning.
Relationships between hero and mentor, unexpected allies, childhood acquaintances, and new friends are sparked from U.A. in one way or another. While some are built over an undefined amount of time, the significance of the relationship can be seen as each group takes on its troubles together.
Endeavor & Hawks
Hawks' mother bought him an Endeavor toy when he was young, and he looked up to the hero for an unspecified amount of years before he became a pro and met Endeavor as one of the Top 10 Heroes in Japan. The current number one and number two heroes likely never expected to work together, let alone get along. Due to Hawks' position with the Hero Public Safety Commission, he has been tasked with an undercover League of Villains assignment, and he personally chose to involve Endeavor when he saw how dangerous the situation was getting.
While Endeavor isn't really the friend type, especially looking down on Hawks for his age, he does partner up when necessary, and, with the information Hawks has shared with him, he considers their working relationship important to the safety of Japan. After their fight with the Nomu, Endeavor gained the ability to read Hawks' expressions well enough to know the issue they will face is larger than expected.
Twice & Toga
When Himiko Toga and Twice fight with Sir Nighteye, Twice's mask splits, causing him to literally come undone. Toga repairs his mask with a handkerchief and encourages him to keep going. In the Meta Liberation Arc, Toga is gravely injured after fighting Pro Hero Curious. It's Twice's turn to come to her rescue, creating a double to give her a blood transfusion.
Twice's eventual death leaves Toga only able to say goodbye to one of his clones and hungry for revenge. There may not be an exact date, but Twice and Toga were friends since joining the League of Villains until Twice's death during the Paranormal Liberation Arc. Although it was a seemingly short-lived friendship, it was a passionate one where Toga later admits to Ochaco that Twice was important to her.
Best Jeanist & Katsuki Bakugo
Despite not often being seen as a great relationship since Bakugo whined throughout his internship with Best Jeanist, the two actually have good rapport after Bakugo secretly began to respect his mentor. They were only together for one week during the internship and were still able to gain a great understanding of each other. Their relationship even leaked over into Bakugo's ability and drive to refuse the League of Villains, as Jeanist explained how vastly different heroes and villains truly were.
Anime fans have yet to learn Bakugo's official hero name, but he has mentioned that he finally chose one and has to tell someone specific before he will reveal it to anyone else—and that someone is Best Jeanist.
Gran Torino & All Might
Retired Pro Hero Gran Torino was a mentor to All Might when he was a student at U.A. Their relationship comes off as rocky because All Might seems to tiptoe around his old professor since he knows about One For All and about his former mentor, Nana Shimura. Gran Torino seems unbothered by it and often calls All Might by his given name, Toshinori, especially when giving him advice on how to help Midoriya.
The two maintain a working relationship when Midoriya brings them back into each other's lives, putting their mentor/friendship at almost 35 years.
Ochaco Uraraka & Izuku Midoriya
Ochaco Uraraka's closest friend would be Tsuyu Asui, but, when it comes to budding relationships, one of the most hinted at romantic relationships is between Izuku Midoriya and Ochaco. Izuku rescued Ochaco from a robot in the entrance exam, Ochaco rescued him from falling at the entrance of U.A., and, each time they come to each other's rescue, they blush uncontrollably.
They've only been friends for two school terms—about one full year—but, as time goes on, their confidence and honesty around one another has been growing. At the Class 1-A vs. Class 1-B event, Ochaco rescued Midoriya from his newfound Blackwhip quirk, and she realized that she's starting to pay attention to him without hesitation.
All Might & Sir Nighteye
This relationship started less as mentor and student and more on an equal ground since Sir Nighteye was All Might's sidekick. Nighteye was 27 years old when he convinced All Might to let him work alongside him. They were friends for eight years before Nighteye saw All Might's death & asked him to slow down, but, when All Might didn't listen, they part ways until Nighteye, at around age 36, asks Mirio to study at his agency.
The two were not on speaking terms for about four years and when Deku approached Nighteye's agency, and it allowed All Might and Nighteye to reconnect temporarily before Nighteye's death.
Shouta Aizawa & Present Mic
Shouta Aizawa is currently a teacher at U.A. high alongside his childhood friend Hizashi Yamada, also known as Present Mic. Aizawa and Mic became friends their first year at U.A. and are now in their 16th year in other's lives.
They were a trio at one point with Oboro Shirakumo and losing him in their second year kept the two teachers close. Mic is even the one that gave Aizawa his hero name "Eraser Head." So, while Mic may poke fun at his quiet yet intimidating friend, they remain close and unwavering.
Mirio Togata & Tamaki Amajiki
Mirio Togata, also known as Lemillion, has been friends with Tamaki Amajiki, A.K.A. Suneater, since the third grade. Mirio has always been a bright spot in Tamaki's life, and, when Tamaki would doubt himself, Mirio would assure Tamaki that he was also an inspiration.
They maintain their friendship when they attend U.A., and, eventually, Nejire Hado joins their friend group, and they become U.A.'s "Big Three," teaching future heroes what it's like to hone in on their power and join the hero industry. Even after graduation, Mirio and Tamaki will have been friends for 12 years with no signs of letting each other go.
Izuku Midoriya & Katsuki Bakugo
"Friends" might not be the right word for what Izuku and Bakugo were as kids. Bakugo "let" Izuku hang out with him because they were four years old, and, at the time, the rivalry was based on Bakugo's ego of his powerful quirk. As time went on, Bakugo's irritation turned into bullying, creating some pretty sad moments for Midoriya. Even with growing up together and attending the same middle school, it seems the two are finally truly becoming friends after 10 years.
The development in their relationship can be attributed to Izuku's understanding of why Bakugo is constantly fighting to be number one and Bakugo's understanding of Izuku's late quirk appearance. All Might also could be considered a good influence on their relationship since both students look up to him.
Izuku Midoriya & All Might
Before Izuku met All Might, he looked up to him for 13 years. Izuku met him with nearly perfect timing, as he was about to transition to high school and wanted to go to U.A., All Might's Alma Mater, and All Might was dealing with his ever-approaching loss of power as he searched for a successor.
Their relationship started in early April when Izuku was 14 years old. They trained together for 10 months before U.A.'s practical entrance exam, and, as of Izuku's third term at the prestigious school, he will have known All Might for 2 years. Two years doesn't seem very long, but, in the grand scheme of what these two heroes have endured, it makes their relationship one of the strongest in the franchise.