Katsuki Bakugo/Relationships

Izuku Midoriya
Katsuki and Izuku were playmates during their childhood. However once Katsuki learned Izuku didn't have a Quirk while he himself manifested a powerful one, he had since always considered the latter as a hindrance in his path to becoming the greatest hero, bullying Izuku for more than ten years. Although he felt superior to Izuku, there are times where he feels that Izuku was making fun of him, such as when Izuku saved him or due to Katsuki thinking Izuku is "hiding the fact that he had a Quirk all this time".

After his loss to Izuku in the Battle Trial, Katsuki sees Izuku as his arch rival and has always shown hostility towards Izuku whenever he interacts with him. Katsuki's antagonism towards Izuku only intensified after seeing Izuku improved on his use of Quirk. His antagonism is so great that even when teamed up with Izuku, Katsuki ignored whatever he suggested and went as far as to attack him for trying to help him and stated that he doesn't need his help. However, after Katsuki stated to All Might he would rather lose than accept help from others, Izuku punched him in the face stating he's not the type to just give up like that. Though reluctant, Katsuki got the message and finally worked together with Izuku and willingly protected him from All Might so he could get to the finish line.

After Katsuki was kidnapped by the League of Villains, Izuku was part of the Rescue Bakugo Team. Katsuki is hinted at piecing together Izuku's relationship to All Might.

After the Hero License Exam, Katsuki called out Izuku to Ground Beta where they first fought. There, Katsuki told Izuku his deduction on All Might and All For One, and deduced Izuku's Quirk was given by All Might. Katsuki, wanting to figure out why Izuku was given All Might's power, attacked Izuku, proclaiming they were going to fight. With this, it seems that, no matter how much he hates it, that Katsuki does at least acknowledge Izuku's abilities. Katsuki seems to begrudgingly at least respect Izuku as a fighter and a rival, going as far as to point out a weakness of the latter's Shoot Style.

Interestingly, despite his malice towards Izuku, Katsuki has at two occasions shown his true feelings in front of him. Once, after admitting defeat to Izuku and his realization of how 'powerful' he truly was at U.A. and the second occasion when he confessed his anguish towards All Might's current state. Basically Katsuki learns to see just how jealous he is of Izuku and slowly start to build their friendship back up.

Izuku always refers to Katsuki as Kacchan (かっちゃん).

Eijiro Kirishima
Katsuki seems to get along well with Kirishima, despite their differing personalities. Eijiro looks up to Katsuki's explosive attitude, often interpreting his actions as manly, something Eijiro appears to highly value. Although, he's not above getting frustrated with Katsuki's tendencies, as seen when Eijiro tried to get him to cool off after Monoma insulted them during the cavalry battle. Although Katsuki at first didn't give Eijiro much attention, he seems to appreciate their Quirks' compatibility with each other, as he accepted Eijiro's proposal to form a team during the Human Cavalry Battle. However, at the beginning of the Sports Festival, Katsuki called Eijiro "hedgehog hair" (despite having spiky hair himself), which bothered Eijiro. Overall, Katsuki gets along with Eijiro, and as such Eijiro is the only person in Class 1-A Katsuki actually respects and would go as far as calling Eijiro a friend. As noted by Izuku, Eijiro is the only one in their class who can call out to help Katsuki without hurting Katsuki's pride, which was proven true and shows that Katsuki indeed does view Eijiro as a friend. During the Hero License Exam, Denki stated that Katsuki had reduced the power of his explosions to avoid harming Eijiro and they have even been seen studying together. When Kirishima openly voices his self doubts, Bakugo reminds Kirishima of times when he has committed to being strong and times when he has actually been strong. Although for an ordinary person this would seem trivial, Bakugo's usual personality  and the fact  that this is the first time that Bakugo has directly complimented and supported another character in the series,  leads us to believe that his relationship with Kirishima is more personal than his relationship with others.

Shoto Todoroki
Katsuki sees Shoto as another rival and someone that he needs to defeat to become Number One. The latter has occasionally shown not to be scared of Katsuki in the slightest, casually making comments that could tick the other off. When Shoto and Izuku talked to each other after the Human Cavalry Battle, Katsuki secretly overheard Shoto's backstory, with a seemingly surprised expression on his face after hearing it. Despite hearing Shoto's tragic backstory, Katsuki showed no sympathy towards him, although his statement about not caring about Shoto's problems or feelings could also be taken to mean he wanted the two of them to be able to fight without being held back by anything. After their battle in the Sports Festival, Katsuki despised Shoto due to him not giving him a battle worthy enough of being called Number One. Katsuki's anger caused him to be fully restrained during the closing ceremony of the Sports Festival so he wouldn't release his fury onto Shoto.

However, Katsuki seems to have let go of his grudge as the two were seen having a normal conversation during their training at the lodge cabin. In other words, Katsuki and Shoto appear to be neutral with each other, with the latter not hesitating to interact with Katsuki in a relaxed way.

Ochaco Uraraka
Katsuki doesn't bother to interact with Ochaco, most likely due to her being friends with Izuku. They first interact during the Sports Festival tournament when they have to face each other in the first round. Katsuki, in his own way, had offered Ochaco the chance to withdraw since would show her no mercy even if she is a girl. Before the end of their match, Katsuki used her last name before finishing her off, indicating that Katsuki respects Ochaco's perseverance (as he usually doesn't use peoples' names). Katsuki even went out of his way to say that Ochaco wasn't fragile, even when his classmates said that she was. His nickname for her is "round face."

In an omake, Ochaco talked with Katsuki about his relationship with Izuku.

Toshinori Yagi
Similarly to Izuku and Shoto, Katsuki idolized All Might as a child. While very little of this respect and admiration remains in present time, it seemed to have a strong impact on Katsuki's belief in what a hero should be. Despite Katsuki's aggressive nature, All Might repeatedly attempts to guide him whenever possible. Although his advice often fallen on deaf ears and All Might is often unsettled by Katsuki's behavior, be it his aggression or his reckless drive.

Unfortunately, despite his past admiration for the renowned hero, Katsuki does not hesitate to either insult or challenge All Might to a fight, refusing to run away when he fought him, only to suffer a humiliating defeat, just as Izuku stated. He was also angry and embarrassed that he had to be saved by All Might when he was kidnapped and even refused to thank him. Despite his antagonistic attitude towards his former idol, Katsuki did show concern when All For One attacked him, showing that he at least somewhat care for him. After learning of his true form, he still believed in All Might's ability to be a hero and refused to lose his faith in him. However, with All Might in retirement, Katsuki seems to have gotten a clue about All Might's relationship with Izuku, going as far as to ask him about what he is to him. Even still, Katsuki did thank All Might for saving him from the League of Villains.

In the end, Katsuki's admiration and concern for All Might was revealed to be larger than he had previously shown. He admitted to Izuku that he blamed himself for All Might's retirement and current state after being kidnapped and after the battle with All For One. This had a lasting impact on him as he did not know what to do after the fact. All Might confronted Katsuki after his second battle with Izuku, telling Katsuki that he is not responsible for his pitiful state and apologized to him as well as told him the truth about One For All.

Katsuki's Mother
Katsuki doesn't seem to respect his mother, as he insulted and threatened her in front of his teachers. However, these threats are more like his usual, childish reactions to everything and not genuine.

His mother has a similar attitude towards her son, as she often yells back at him and insults him too. She is aware of her son's terrible behavior and disapproves of it. She blames on the fact that her son has a strong Quirk and receives a lot of praise for it, which seems to make Katsuki angry about her statements. Katsuki's mother approves of her son going to U.A though, as she believes the school will see him for who he truly is.

All Might also comments that their family is the most dysfunctional one he has ever seen.