Since they happened to be seated one behind another in class, they became good buddies and often make comments to each other.
At the beginning of the cavalry battle ark when Katsuki makes a remark about the importance of winning, Eijiro is visibly moved by Katsuki's words and calls the other manly. During the cavalry battle, Eijiro approaches Katsuki in an attempt to form a team with him. Katsuki calls Eijiro "hedge-hog hair" at first but after Eijiro presents himself as rock who will not waver, the two form a team together with Ashido and Sero.
Over the series the relationship between the two improves greatly and Eijiro and Katsuki become close friends. While Eijiro is friends with a wide range of people in his class, he can constantly be seen talking to Katsuki and making an effort to include him in on activities while others would have ignored him. In one case, Eijiro invited Katsuki to go shopping with the class and in another he made attempts at conversation when the class results were handed out.
One of the most significant points in Eijiro's and Katsuki's relationship development was during Katsuki's kidnapping. After it was revealed that Katsuki was kidnapped, Eijiro was visibly distressed and immediately wanted to form a group and rescue him, even buying a pair of 50,000 yen night vision goggles in order to take back Katsuki from the villains. During this arc, Eijiro stated that "When I heard that they were after my buddy...I couldn't do anything!!" which confirms that he views Katsuki as a friend and was distraught upon hearing that Katsuki was kidnapped.
During the rescue, Izuku explains that only Eijiro can take Katsuki's hand and rescue him without Katsuki taking offense and refusing. This illustrates the intense and trusting connections that the two share and reveals that Eijiro and Katsuki are very close as Katsuki would not accept the help of any other person.
After this arc, Eijiro and Katsuki were more connected than previously, sticking close together during the hero license exam and hanging out together in free time. Often when Katsuki's whereabouts are unknown to the rest of class 1-A, they will ask Eijiro for an explanation.
While versing a particularly difficult villain, Eijiro thinks back to a time when he was voicing concerns about his powers to Denki and Katsuki. Katsuki speaks up and attempts to support Eijiro by talking about how strong he was.  Eijiro seems to use this memory to motivate him and allows him to unlock his "unbreakable" state.
Similarly, when Eijiro is versing villains in the lair of The Eight Precepts of Death, he thinks back to Katsuki's words after he has failed to defeat a villain.  This illustrates that Eijiro feels that he has failed Katsuki by not living up to his expectations. Eijiro obviously looks up to Katsuki and feels motivated by him but also feels disappointment when he cannot impress him.
Eijiro and Tetsutetsu initially had a rocky relationship because of their similar Quirks. During the U.A. Sports Festival, they met when they both survived being crushed by a 0-Point Villain. As the festival progressed, Eijiro resented being constantly compared to Tetsutetsu, like when Present Mic gave them similar intros prior to their match against one another. 
After Eijiro defeated Tetsutetsu in an arm wrestling match , he congratulated the latter on a battle well fought, starting their eventual friendship. In Eijiro's next match, Tetsutetsu cheered for him to knock Katsuki out. 
They both proved to be on good terms with each other when they ended up interning together at Fourth Kind's Hero Agency. They were initially surprised to see each other, but instead of lamenting about comparisons, they friendly greeted each other. 
Eijiro and Sero are good friends with each other.
Eijiro seems to be on good terms with Izuku. When Shoto told Izuku that he will defeat him, Eijiro tried to stop any further arguing and when Izuku started to talk negatively about himself, Eijiro tried to encourage him. He also told Izuku that he is envious of his Quirk.
He also seems to admire Izuku's growing confidence and seems to be impressed by his quick thinking and logical reasoning. He also seems capable of understanding Izuku's feelings to some extent, understanding how he felt when he was unable to rescue Katsuki. In more recent chapters, Ejiro and Izuku are shown to be on better terms than previously, often interacting in friendly ways.
Eijiro gets along well with Mina despite not interacting with her as much as he does with his other classmates. The two collaborated together on Team Bakugo during the Sports Festival Arc and seemed to work well together.
In chapter 144, it was revealed that Mina was the source of a lot of Kirishima's self-doubts. The two went to the same junior school. During their senior year, Eijiro tried to stop two students from bullying an underclassman but did not succeed. Afterwards, Eijiro witnessed Mina step in and solve the issue by forcing the student and the two bullies to break dance, diffusing the situation and ending the issue. One of Eijiro's friends point out that Mina is very athletic, outgoing, strong and eye-catching while Eijiro and the others are boring. Eijiro seems to admire Mina for this but also begins to feel self-conscious and envious of the fact that Mina is exciting and heroic while he is not. This is reinforced when he attempts to stop a villain on the same day as the bullying incident but his legs freeze up and Mina stops the villain instead.
However, in spite of these facts, the two are not particularly close, as they are rarely seen interacting with one another.
Eijiro idolizes the Pro Hero: Crimson Riot and desires to become a hero just like him. Eijiro chose his Hero Name "Red Riot" to pay homage to him.
Tamaki is initially somewhat annoyed by Eijiro's optimism, but at the same time compliments him for it, and later compared him to Mirio. Eijiro has a lot of respect for Tamaki, due to him being his senior.
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