The Forelli family is an Italian-American Mafia family based in Liberty City. The Don of the Forelli family in 1986 is Sonny Forelli, who would be killed by Tommy Vercetti, a renegade Forelli family member in Vice City. They had planned to expand their empire "down south", by opening relations with local drug cartels through Tommy Vercetti, but that never happened due to Sonny's death and Tommy's defection. The main base of operations for this once powerful organization was Marco's Bistro before Sonny's death. The Forelli family used to be the most powerful family in Liberty City, but the deaths of many high-ranking members (such as Sonny, Giorgio and Franco) have led to their subsequent downfall over time.
In San Andreas, it was agreed that the Forelli family would own an equal share of Caligula's Casino, along with the Sindacco and Leone families in 1992. However, their part in the deal would quickly end as Salvatore Leone (the Don of the Leone family) ordered Carl Johnson to gun down the Underboss of the Forelli family (Giorgio Forelli) at Marco's Bistro (having already destroyed the Sindacco family's influence in Las Venturas) so the Leone family could fully control the Casino.
In Liberty City Stories, Salvatore Leone mentions Franco Forelli as the Don of the Forelli family at the time, likely taking control of the reigns after Sonny Forelli's death in 1986. Liberty City Stories also reveals a Little Italy district in Fort Staunton that served as the main base of the Forelli family's operations after Sonny's death. They got into a gang war with the Sindacco family after the latter fled Portland - a gang war that the Leone family were only too happy to prolong, weakening both sides. The entire district was destroyed by Toni Cipriani on orders from Donald Love, using plans stolen from Avery Carrington, effectively taking all their assets and power with it. What was once Little Italy would become the construction site disputed by the Colombian Cartel and Liberty City Yakuza by GTA III. It is highly likely that Franco Forelli was killed in the explosion, as he is neither seen nor mentioned thereafter in GTA:LCS and GTA III.
By GTA III, the Forelli family seems to have been weakened considerably, with the killing of several more Forelli members (including Mike "Lips" Forelli, the speculated Don after Franco's death) by Claude on Joey Leone's orders. It is assumed that the Forelli family has been reduced to servitude under the Leone family and their organization on the whole is now considered a brotherhood. At this point in time, the Forelli family's territory is assumed to consist solely of Marco's Bistro, but that might also be under majority control of the Leone family as a Leone Sentinel was seen parked there in Liberty City Stories. It is possible by the end of GTA III, the Forellis would cease to exist. The Forelli family has also been called the Forelli Brothers.
In GTA:LCS, Forelli members don blue/dark red shirts with light blue/white jackets over and carry pistols. In GTA:SA the mobsters (presumed to be the Forelli family) dress in either brown leather jackets with gray pants, light blue shirts with chains or in black jogging suits. In GTA III, they dressed like the Leone family as seen in one of Joey Leone's missions as they were in disguise. In GTA:VC they wear white or red Hawaiian shirts with tan or brown pants.