The original False Face Society appeared in Batman #152 (1962), organized by the Joker disguised as a mysterious mastermind, who held a contest to see which criminal could commit the most spectacular crime while dressed in the costume of another profession. For example: one committed a crime dressed as a deep sea diver, which helped him to escape underwater. They were presumably disbanded after the Joker was exposed and defeated by Batman. Whether the Joker's role as the False Face mastermind led to the creation of the Batman villain known as False Face is unknown.
In 1984, the False Face Society was reimagined for the Bronze Age of comics by writer Doug Moench to be the cult-like gang for his new villain, industrialist-turned-mobster Black Mask. Like their employer, each member wore a mask to conceal their appearance and to give themselves a new identity, as the mask, in effect, "became" their new, true faces. Black Mask's philosophical use of masks inspired fanatical devotion from the False Face Society, and those members who questioned their boss' views were swiftly executed by other False Face Society members.
When Gotham City was decimated by an earthquake in the events of Batman: Cataclysm, which then led to Gotham becoming a lawless No Man's Land, Mask's insanity caused him to turn the False Face Society into a full-blown cult, and demanded that they abandon their masks in favor of self-mutilation, to deface their own faces and bodies just as Gotham itself was defaced. After Mask's defeat and capture, the False Face Society scattered, some being executed by Two-Face and the Tally Man, while others reformed.
In the time following NML, Black Mask seemingly abandoned the False Face Society as his army, choosing instead to surround himself with standard mobsters, hoods, and henchmen. It is unknown whether the False Face Society was disbanded either officially or unofficially, or whether or not they continue to operate following Black Mask's death at the hands of Catwoman.
The New 52
For more information see: Detective Comics Annual #1
In the New 52 Black Mask never truly disbanded the False Face Society, instead when he was captured he put Edgar Dempsy in charge of hiding the masks, the Society wore. When Black Mask broke out of Arkham, during the events of The Night of the Owls, he sent Mad Bull to retreive the masks from Black Otter Carnival, but they had been taken already.
Black Mask sent the Dwarf to retrieve Dempsy for questioning, and Dempsy lead Black Mask and his team of sideshow freaks to the Gotham Museum. There it was revealed the mask were made from the same stuff as Black Mask's mask and gave Black Mask control over the wearer.
The Dwarf was revealed to be Mad Hatter, who was using the masks for his own personal gains. The Black Mask killed Dempsy and tried to kill Hatter, but Batman showed up and stopped the fight. In the confusion, the Black Mask's mask was lost and Hatter got away.
It is unclear who is ruling the False Face Society now that Black Mask is back in Arkham and the Hatter can control the wearers of the masks.
On the Future State Earth, a False Face Society was being led by a new Mr. Toad. He was distributing a "false face serum" that changes people's faces at a genetic level into that of an animal. This False Face Society is fighting back against the surveillance state of The Magistrate, who has outlawed masks.
In Other Media
The False Face Society appears in the second season of Batwoman.