Before Arkham Origins Incident
Prior to Christmas Eve, the leader of the Maroni Family was apprehended and tried. Although the case' conclusion is unknown, Maroni was indicted with at least four charges. The police denied Batman's involvement in the case, although this proved to be false, as the vigilante's closed case 151 was a full investigation on Maroni.
Before Arkham City Incident
At some point the Maroni family gathered at their restaurant to talk about how to finally win the war between themselves and the Falcones. As they talked, the building was surrounded by Carmine Falcone's men, who opened fire on the building. Most of the Maronis inside were killed, and their leadership eliminated. All of the remaining Maronis were incarcerated in Arkham City.
Arkham City Incident
Although inmates within Arkham City, the Maroni's paths' never crossed with Batman's on the night that he was sent there. Batman did, however, have to locate their restaurant to solve a riddle left by The Riddler.
Arkham Knight Incident
Sal Maroni, one of the members, had somehow managed to both survive the Falcone's attacks and Protocol 10, although he ultimately was killed by the vigilante Red Hood.