Carlisle was the first of the Cullens, and made most of them into vampires.
Unlike most vampires, he is not tempted by the scent of human blood, which allows him to be a doctor and to keep himself to a "vegetarian" diet.
He believes this is because he brought compassion from his life before, just like Edward got mind-reading, or Alice got Future-telling.
He married Esme after he saved her from commiting suicide, and since then, all the people that he has changed have become their "adopted children."
For a short time before he changed any people into vampires, he lived with the Volturi, but then decided that he wanted to leave to the "New World" (he became a vampire in the 1640s).
The first person he changed was Edward, because he was dying of the Spanish Influenza.

Carlisle is the only of the vampires that can stand the scent of human blood, since he has been a vampire for so long, and because he works as a doctor.