The Gotham City Crimelords were mob bosses who worked in Gotham City. Carl Grissom acted as the head of them.
After Jack Napier, rechristened the Joker, killed Grissom, he took his place with the cover that Grissom was in hiding. Joker then relayed "orders" on Grissom's behalf to "run [Gotham City] into the ground" starting with the bicentennial celebrations. However, several of the crime lords, notably Vinnie Ricorso and Antoine Rotelli were suspicious of Grissom's orders, namely because they never heard it from him directly, and because of Napier's suspiciously wide grin. When Rotelli refused, Joker, under the pretense of shaking his hand to avoid a gang war, killed him via a joy buzzer to make an example out of him, while having his own men point storm the meetings and point their Thompsons at him. He then had everyone depart, although not before Vinnie, horrified by how he killed Rotelli as well as his joking reaction to it, denounced him as crazy. The Joker then decided, while "talking" with Rotelli's charred corpse, to "grease" the rest of the mob summit, with Vinnie proceeding to die shortly thereafter while retrieving finances from Grissom's account as part of a "personal favor".
It was never revealed what became of them after the Joker sent them away or after the first film. Though it was likely that they lost most control over the Gotham Underworld thanks to Batman and the super-villains that have emerged over the years, or were murdered by the Joker under the post-mortem "suggestion" of the then-recently deceased Antoine Rotelli.