With the assistance of Kaname Kuran, Headmaster Kaien Cross (also known as a legendary Vampire hunter) founded Cross Academy under the influence of Juri Kuran's dream of having humans and vampires co-exist together. Kaien had mainly done this because he once made the decision to kill the Kurans, and he had stalked Juri, waiting for an opportunity to do so. He was, however, instantly defeated by her during their confrontation, and a bargain was made that he would create Cross Academy peacefully.Thus, Cross Academy was born. Though some vampires gave in occasionally to blood-thirst and disobeyed the rules, they would receive a large amount of punishment from Kaname Kuran, the Academy's pureblood and the Moon Dorm president over the entire Night Class. Most vampires adore and fear Kaname, so his commands are usually obeyed. There has not been a noted occasion where Kaname had to actually use his pureblood powers to maintain order in the Night Class.
The fact that vampires are attending the Academy is a complete secret from the Day Class humans. They are not to know the existence of Vampires, and if they do find out, their memories are erased on the spot, provided there is a very good reason not to (this comes into question mainly in season 2, "Guilty"). The existence of the vampires must be kept a secret, in Kaien Cross's mind, else humans would bee too frightened to be near the academy, not to mention the animosity that would arise. The goal of the Academy is for humans and vampires to co-exist together. Yuki Cross and Zero Kiryuu are the Guardians in charge of protecting this secret.
The duty of the Guardians is to make sure the Night Class doesn't cause any trouble for the Day Class students and vice versa, and preform duties as the Headmaster requires of them. This usually entails the night patrols he assigns them (to make sure no Day Class students have snuck out of their dorms while the Night Class is in session), as well as the dawn and evening tradeoffs between the two classes to the main Academy building.*SPOILERS! DO NOT READ PAST THIS POINT IF YOU CARE!*
Unfortunately, things do not stay peaceful forever. People within the Vampire Hunter's Society and the Vampire Senate begin to interfere in the Academy's business, and two powerful purebloods, Shizuka Hio and Rido Kuran, each come to the academy on business of their own.
Shizuka possesed the body of one of her young relatives, Maria Kurenai, to infiltrate the academy Night Class, looking for Zero Kiryuu, whose family she had attacked when he was a child. Her intention was to kill Kaname Kuran and steal the powers his blood contained. She was eventually discovered and killed by Kaname, and the murder was blamed on Zero.
This event triggered the involvement of the Vampire Senate, who came to the academy to kill Zero for the murder of a "sacred" pureblood. They are eventually halted and destroyed by Kaname Kuran.
Even further disruption at the academy occured at the appearance of Rido Kuran, who intended to find Yuuki Cross and consume her blood. He brought an army of Level E vampires with him, attacking any student without hesitation to find her. The Night Class, rallied by both their own initiative and the encouragement of Kaname Kuran, defended the academy from the attacks, but of course the secret had already been revealed. Later, the Day Class votes strongly to maintain their memories of the Night Class, and are granted their request.
After the ordeal is over and Rido Kuran is defeated, many portions of the academy are left in rubble and ruin, and the school is shut down. However, later in the manga portion of the series (post-"Guilty"), some of the school is rebuilt and Yuuki Cross, now Yuuki Kuran, attempts to reinstate the Night Class, and intends to reopen the school as a whole, following in Kaien Cross's footsteps.