The Mob, also known as Falcone's Mob, was once a major power in Gotham City and was headed by Carmine Falcone, composed of Italian mobsters. Prior to being run by Carmine, the Mob was known as Calabrese's Mob due to being headed by Rex Calabrese. The corruptness of the Mob allowed them to take over the GCPD simply by getting them to hire as many corrupt officers as possible. The rise of the Mob allowed the Red Hood Gang to take over Gotham, though the coming of the Batman brought down the fall of the Mob. For a short time, Sal Maroni was in charge, but this did not last very long.
The Mob then moved to Hong Kong, where they ended up setting up a very extensive crime network. However, it only lasted so long as Falcone later returned to Gotham. The Return of the Mob to Gotham was unique, as they quickly began to secure the city. Due to the efforts of Jason Bard, however, Falcone's Mob was forced to return to Hong Kong. This second fall, allowed for Selina Calabrese to reform Calabrese's Mob.
Prior to the rise of the Batman, the Mob's fiercest competitors were the Red Hood Gang and the Irish Mafia. Following however, the Mob easily disbanded. It was succeeded by Penguin's Empire.