Savannas are also a cross breed between a domestic and a wild cat. They are bred from Servals and rarer and bigger than Bengals. With both breeds, only F4's (4 generations from the original wild cat) are considered domestic cats.
Bengals originated at Loma Linda University which was trying to see if the wild Asian Leopard Cat's immunity to Feline Leukemia could be bred into domestic cats so they bred ALCs with domestic tabbies. The male offspring were sterile until F4 but the female offspring were fertile. A woman named Jean Mills took in the Loma Linda Bengals and bred them as a new domestic breed.
The ALC is a shy cat so Bengal breeders select cats that are very social with humans and other animals for breeding. Bengals are considered similar to Jack Russell Terriers -- they are more active and mischievious than most cats so owners have to want an active breed.