The family was founded by Tomaso Moretti, who was later assassinated during the Vinci-Moretti War. The family then became headed by Don Carlo Falcone. During Falcone's reign, the Falcone's became a ruthless rising star in the Empire Bay underworld. They became the second most powerful family in Empire Bay and were the family that Vito Scaletta and Joe Barbaro would eventually join. However, due to the death of Falcone and many of their men, they were weakened significantly. As Eddie Scarpa was Falcone's underboss, it is possible that he became the new boss after Falcone's death.
By the game's end, only Vito and Harvey are confirmed alive in the family, as Balls is retired and Joe is most likely dead. Eddie's current status is unknown. It's also possible that as a result of killing Carlo Falcone under Leo Galante's orders Vito ended up in the Vinci Family.