Up until his disappearance in "End of the Beginning," Ozpin served as the headmaster of Beacon Academy.
Ozpin is a member of a group whose goal is protecting the world from dangers that are kept secret from the public. Other members of the group include Glynda Goodwitch and Qrow Branwen, as well as the leaders of the other three academies - James Ironwood of Atlas Academy, and the respective headmasters of Haven Academy and Shade Academy.
Glynda is a fellow staff member at Beacon Academy. Despite being often seen alongside him when addressing students, her only interaction with Ozpin until "The Emerald Forest, Pt.2" was in "Ruby Rose" to note Ozpin's interest in Ruby Rose and express mild exasperation at his desire to have Ruby enrolled.
Due to the blunt and honest manner in which she usually speaks to him, it seems as if the two have known each other for a while; although, their exact history has not been mentioned in the series thus far.
Ozpin has known Qrow for years, as implied in Ruby's interrogation in "Ruby Rose". Ozpin was definitely present on Qrow's first day at Beacon Academy. In "Black and White", the two men are continuing an apparently-secret correspondence regarding someone code-named "The Queen".
When the two meet with Glynda and Ironwood in Ozpin's office, Qrow mentions that Ozpin invited Ironwood into the group's inner circle, implying that Qrow had Ozpin's trust far earlier. After Ozpin disappears, Qrow sees himself as the one to step up and take responsibility in Ozpin's place. This includes taking over Ozpin's Cane, which he later gives to Oscar Pine. This act indicates Qrow's awareness of more secrets about Ozpin than the show has revealed, particularly with the words "It's good to see you again, Oz."
Ozpin and Ironwood seem to be very good friends, speaking in manners unseen with most others. This indicates a rather personal level of familiarity. However, Ironwood's methods and views about security tend to clash with Ozpin's, resulting in the two being regularly at odds with one another. Though Ozpin considers the general misguided, he also notes that his heart is in the right place.
Ironwood comments that he has served under Ozpin for years as part of his secretive group; despite their differences, Ironwood still answers to Ozpin.
Ozpin seems to take a special interest in Ruby. When the two first meet, he is intrigued by her silver eyes, knowing about her linage, before commenting on her level of skill with her scythe, Crescent Rose. He also seems interested in Ruby's motivation for becoming a Huntress, in that she wants to help people. He is so impressed by Ruby that he allows her to skip two years at Signal Academy in order to enroll at Beacon Academy.
Even after her enrollment he continues to watch over her, completely ignoring Glynda's report during the Beacon Academy Initiation in order to watch Ruby's progress on his Scroll. He is also seen observing her in "Black and White".
During the year at Beacon, Ozpin appears at her side a number of times. After Weiss Schnee starts making Ruby question her appointment as team leader, Ruby asks Ozpin whether he made a mistake appointing her as team leader. The headmaster gives Ruby a pep talk, advising her that being a leader means acting her best so that she will be respected by her teammates. He then confides in her briefly, stating that he's "made more mistakes than any man, woman, and child on this planet". At the Beacon Dance, he advises Ruby to enjoy herself, pointing out that fighting and dancing aren't very different.
He also covers up for Ruby, cutting off Glynda's question when Ruby tells him of a possible hideout in the southeast of Vale despite Ruby previously saying that Cinder did not say anything to her.
After Team RWBY is unable to get their mission in the southeast, Ozpin hints that he is aware that they have been up to extracurricular activities. He makes Ruby self-conscious and uncomfortable while listing unexplained events from "Black and White", "Extracurricular", and "Painting the Town", all while claiming he'll never find exact answers. Ruby's mood changes, however, when he volunteers to bend the rules for them to get their mission, since he suspects that they would make their way there anyway.
Ozpin is aware that Blake is a Faunus, and also seems to suspect Blake having some affiliation with the White Fang as he questions her on how she had known where the they would attack. In addition, he notes that she is one of only a few people who managed to enter Beacon Academy without the years of preparation to pass the rigorous entry exam.
He ends the questioning by offering her a listening ear, should she ever need to talk to him.
Ozpin has thought highly of Pyrrha since she began attending Beacon. He thinks of Pyrrha as strong, intelligent, caring, and ready to be a guardian figure.
Ozpin and Salem are aware of each other's presence, even before the beginning of the show proper as proven in the opening narration of "Ruby Rose." While Salem seems intent on destroying humanity, Ozpin holds a contrary view, placing both of them at odds with each other.
Cinder Fall is the main enemy of Ozpin and his group during the first three volumes. She successfully steals the Fall Maiden's powers that Ozpin's group tries to protect. They both meet face to face in "Heroes and Monsters" where she expresses her disdain for him and prepares to fight against him. In "End of the Beginning", both finally clash in the vault underneath Beacon, resulting in Ozpin's disappearance. Cinder later reports to Salem that she killed Ozpin, though Salem questioned her at least one more time as to the truth of this.
Ozpin informs Oscar in "Kuroyuri" that Hazel is a man from his past who is not to be taken lightly.
A fellow staff member at Beacon, Port shows a deep trust and admiration for Ozpin when defending him to Weiss, stating that he served under the headmaster for years; in all that time, Ozpin never led Port astray.
Ozpin first speaks to Oscar in "Family", but it is not until "Punished" that it is revealed the conversation takes place inside Oscar's mind. Ozpin informs Oscar that their Auras and souls are combined and Oscar's thoughts are now also his.