The Kiryu family was a vampire hunter family. They are very well known for their skills in killing vampires. They are also one of the only hunter families in history to have ever given birth to living twins, Zero Kiryu and Ichiru Kiryu. This is almost unheard of due to the "curse of the hunter twins," for a hunter to usually get pregnant with twins, one would devour the other to gain it's strength.
The Pureblood vampire Shizuka Hio was brought up in a cage, because members of the Hio family had a history of their members going berserk. While there, she was brought human sacrifices as her food. She fell in love with one of the sacrifices and, instead of killing him, turned him into a vampire and gave him her blood so he wouldn't fall to Level E. Her fiancee, Rido Kuran, whom she detested, put her lover's name on the Vampire Hunter's execution list under the mistake that he was in fact a Level E, though in truth he wasn't.
It was the Kiryu's mission to kill him off, which they did.
This prompted Shizuka, in a heartbroken rage, to murder the two parents, bite Zero, thereby turning him into a vampire, and make Ichiru her devoted servant later.