Issei, at first, hated Azazel because he was a Fallen Angel, but learned later on that he is a good man. Azazel later became the Occult Research Club's advisor in Volume 4, and aided the Gremory team on how to better improve themselves as a team. He also helped out in progressing Issei and Kiba's Sacred Gears, as well as helping Issei learn how to achieve Balance Breaker. He also shows a great deal of concern for Issei after his death, but was relieved to hear that his spirit was alive. As time has passed, they now seem closer to each other as they are usually seen together while dicussing things regarding the flow of their lives.
Azazel and Rias' relationship is not clear, but they seem to have a good friendly relationship.
Akeno initially hated Azazel because Azazel is a Fallen Angel like her father. Azazel, on the other hand, cares a lot for Akeno because she is the daughter of his good friend Baraqiel, but also specifically because he feels guilty about her mother's death. He even protected her behind the scenes during her youth before she met Rias Gremory. Azazel believes that he was responsible for it since it was him who called Baraqiel out on a mission that day, thus leaving Akeno's mother undefended. Azazel treats Akeno like his own daughter and has asked Issei to protect and take care of Akeno on multiple occasions.
Much like with Issei, Azazel serves as a mentor figure to Asia for both her Sacred Gear training. Azazel also helped Asia to form a pact with Fafnir after ending his pact with Fafnir.
Like Issei, Azazel helped Kiba in progressing his Sacred Gears. Azazel and Kiba's relationship is not clear, but they seem to have a friendly relationship.
Azazel and Koneko's relationship is not clear, but they seem to have a good friendly relationship.
Azazel and Xenovia's relationship is not clear, but they seem to have a good friendly relationship.
Azazel and Vladi's relationship is not clear, but they seem to have a good friendly relationship.
Azazel and Irina's relationship is not clear, but they seem to have a good friendly relationship.
Azazel and Ravel's relationship is not clear, but they seem to have a good friendly relationship.
One of Azazel's closest friends, Azazel cares deeply for Shemhazai while Shemhazai respects him.
One of Azazel's closest friends, Azazel cares a lot for Baraqiel and feels guilty for having Baraqiel help him which indirectly lead to Baraqiel's wife, Shuri Himejima's death and constantly tries to find a method to compensate Baraqiel. Baraqiel himself doesn't seem to blame or hold any grudge against Azazel, still considering Azazel as his close friend.
Azazel has a respectful relationship with Sirzechs since they were both representatives for the treaty in Volume 4. Since then, they have gotten along, even working together to deal with situations like the Diodora incident and calming Issei down to release him from Juggernaut Drive in Volume 6. They also developed a business relationship for the Oppai Dragon franchise.
Due to his ownership of a Longinus and powers inherited from Lucifer's bloodline Vali was viciously abused by his father due to his father's arrogant pride as a Lucifer's descendant along with the instigation of his grandfather, Rizevim Livan Lucifer. After Vali ran away and was founded by Grigori Azazel was deeply sympathetic towards Vali's suffering and took to himself to raised Vali personally, acting as his surrogate father. Azazel sees Vali as his son in additon to teaching Vali how to master his powers and Sacred Gear, also taught Vali many other fun and joyful things in life such as fishing and taking him for a drive, Azazel cares deeply for him and he was deeply hurt by his betrayal despite expecting it. Vali himself reciporated Azazel's care with gratitude and also considered Azazel the perfect father he has always desire. Thus Vali can be become incredibly enraged when Azazel is badly hurt, such as during the battle against Cao Cao. And Vali was greatly saddened when Azazel leaves him to fight Trihexa.
Azazel has a deep rivalry with Michael even before he became a Fallen Angel. This is mainly because Michael once revealed Azazel's Artificial Sacred Gear's design throughout Heaven without Azazel's permission and was made fun of because of it. Despite their rivalry, Azazel cares deeply for Michael as an ally and prefer not to involve Michael in the eternal battle against Trihexa if possible.
Azazel has perverted thoughts for Gabriel, having fantasies about touching Gabriel's breasts ever since he was an Angel. Azazel has stated he would not have minded becoming a Fallen Angel simply from touching Gabriel's breasts. During the Sports Day between the Three Factions, Azazel encouraged Issei to use Dress Break on Gabriel as he also desired to see Gabriel's naked body.
Azazel hates Hades because Hades despises the Devils and Fallen Angels. His hatred towards Hades intensified after Hades nearly caused Issei's death by lending Samael to the Hero Faction and Shalba.
Azazel distrusts Indra greatly, due to Indra keeping secrets about Cao Cao, and suspecting him to be secretly helping the Hero Faction.
Azazel seems to trust Shiva when he requested to him to stop Trihexa, believing Shiva`s strength can stop 666 once it awakens. They have shown to get along well with each other and go fishing when Azazel appeared in a certain country with Shiva. When Azazel asked Shiva to stop Trihexa when it awakens; which Shiva accepts since he is the only one who can, with Ophis missing and Great Red not accepting. Shiva is shown to honor Azazel and calls him a hero, naming the World Rating Game after him.
Like Vali, Azazel completely despised Rizevim for the latter's atrocious and evil nature. When they met each other in Romania after many years, Azazel was so enraged at the sight of him, that he smashed a nearby wall to vent his anger. When Rizevim was about to be killed by Vali, Azazel gleefully mocked him without hesitation. After Trihexa was revived, Azazel was determined to end Rizevim's legacy of chaos even at the cost of his own life.