Gran Torino and Nana Shimura were close friends. He became a teacher in U.A. in order to train Toshinori solely because of a promise he had made to her. He still mourns her death even years on and after learning that Tomura Shigaraki is her grandchild, he vowed to find him and save him.
Gran Torino taught Toshinori (better known as All Might) as a teacher in U.A. and knows Toshinori's secrets. He seems to have left Toshinori nervous from his past training with his mentor to the point he shook when telling him to Izuku. Also, he has a habit of calling All Might by his given name when they converse.
He is shown to be very cautious of his pupil, going as far as to warn him of the possibility of All For One returning and telling him to tell Izuku everything about him and One For All to prepare him. He also expressed his pride in his pupil for defeating All For One a second time while being the Symbol of Peace one last time.
After All Might discovered Tomura Shigaraki was Nana Shimura's grandson, Torino stopped him from going after him as it would be fruitless to try in reasoning with a criminal and All Might accepted his teacher's words.
Since he knew about One For All and was All Might's sidekick, Nighteye is acquainted with All Might's mentor. Nighteye seems familiar with Gran Torino enough to perceive his signature erratic jumping that Izuku copied.
Gran Torino was present during All Might and Nighteye's falling out. He decided to use Izuku as a means of mediating the relationship between the two, showing he cares about Nighteye. The two later spoke and Nighteye asked him if the reason he directed Izuku towards him was to mediate his relationship with All Might. Gran Torino denies it and says it was just a thought that crossed his mind and asks what he thinks. Sir says they are both similar including the madness in their core that he could never understand.
Gran Torino requested Izuku to be his sidekick so that he can teach Izuku about the One for All Quirk. Gran Torino and Izuku were off to a bad start when they first met, with Gran Torino putting up a façade of being senile and Izuku being disappointed with having to train with someone who was no longer functional. But right after Gran Torino dropped his facade and showing Izuku what he was capable of, Izuku started to gain respect for Gran Torino, politely calling the elderly Hero Mr. Torino. 
Gran Torino has shown to be impressed with Izuku, stating that All Might chose a fine successor. Torino also protected Izuku from a Nomu while Izuku was worried for him.
Gran Torino has shown to be impressed with Izuku, stating that All Might chose a fine successor, due to Izuku's quick thinking and potential. As they parted ways, Gran Torino asked him his and Izuku replied it was Deku, with Torino becoming the second person to make Izuku proud of his nickname.
Gran Torino holds a grudge against the user of All For One for murdering Nana Shimura, his close friend. He became part of the Hideout Raid Team in order to find out more about All For One's whereabouts, joining Toshinori when he started fighting the villain.