Yuuto is very grateful towards his master, Rias, for saving him after he died from the project called "The Holy Sword Project". Being faithful to his status as a Knight, Yuuto is very loyal to Rias and calls himself "Rias Gremory's Sword". While he sees her as an elder sister, he doesn't feel comfortable calling her onee-chan, despite Rias wanting him to.
Issei, at first, disliked Yuuto, mainly due to his good looks and popularity with the girls, but as time passed they became good friends. Yuuto claims Issei to be his best friend as Issei was the one who helped him let go of his rage against the Holy Swords.
When Issei died, Kiba, much like his peers from the Occult Research Club, was greatly saddened. But, however, despite clearly wanting to avenge him, Kiba managed to restrain his emotions and prevented them from getting the best of him. This was due to him remembering the promise that he once made with Issei; that should one of them die someday, then the other would protect the girls in the Gremory group with all their strength. Yuuto, then, fought against Siegfried and was highly enraged when he exclaimed that "Hyoudou Issei died in vain" giving Yuuto, alongside other members of the Gremory group, the required drive and motivation to finally kill him off.
Being his first best friend, comrade, and rival, Issei's existence means a lot to Kiba. Evidenced multiple times throughout the series, this was especially proven when Yuuto experiences an emotional turning point after Issei's "death" in Volume 11.
Originally, Yuuto and Xenovia were on bad terms due to Yuuto's hatred of the Holy Swords and Xenovia's position as a Church Exorcist and an Excalibur wielder. However, after Yuuto obtained the Sword of Betrayer, and Xenovia became Rias' Knight, the two of them set aside their differences, and have grown closer ever since. They have also begun respecting each other's skills as evidenced when they decided to train together in order to hone their combat abilities.
Yuuto and Akeno have a neutral relationship with each other. They are both loyal servants to their master, Rias Gremory. Since Akeno is the Queen in their group, Yuuto treats her with a high honor, respect, and honesty.
Both Yuuto and Koneko are shown to share a close relationship with each other. This was shown in Volume 3 when she was willing to go along with Issei's plan of destroying the remaining Excalibur fragments by teaming up with Irina and Xenovia, without Rias' permission, all in order to keep Yuuto from becoming a Stray Devil.
Both Kiba and Gasper live together in a mansion close to Issei's house. When Gasper was still a shut-in, Kiba, along with the rest of the group, helped him gain more confidence in himself and his power.
He is Yuuto's swordmaster. Kiba has shown to have much respect towards Okita and still call's him "Master" despite Okita teaching him swordsmanship, no longer.
After losing to Yuuto in their master's Rating Game in Volume 5, Tsubaki has developed romantic feelings for him to the point of her losing her usual calm demeanor when in front of or at the mention of him. Yuuto is currently unaware of her crush towards him.
Arthur became, as of Volume 12, Yuuto's rival after being impressed by him, his Holy Demonic Sword and obtaining Gram as well as the rest of Siegfried's Demon Swords after defeating him. Seeing him as a worthy opponent for his Holy King Sword, Arthur tells Yuuto that he will battle him when Vali has his fight with Issei.
Kiba hates Freed with a passion as shown both in the light novels and the anime. When he finds out in Volume 4 that Freed was experimented on to wield a Holy Sword, he feels a certain amount of hatred against him due to the fact that his once fellow comrades had previously died, being branded "failures" by a similar Holy Sword experiment. Yuuto is also strongly disgusted by Freed's vulgar words and showed no signs of remorse after finishing him off in Volume 6.
Tosca was a close friend of Kiba's that survived the ordeal that was the Holy Sword Project. When she finally made her return years later, Kiba was so overjoyed by the fact that she had survived that he ran and forcibly hugged her.