When the Mob took over the GCPD, they became untouchable, with only low ranking members being imprisoned. This allowed Gotham to be overtaken by crime, mostly by several fledgling gangs who arrived to try and forge their own name in Gotham. The only one of these gangs that achieved the success they desired was the Red Hood Gang, who made their trademark through the pill shaped helmets that they wore. Growing so large and dangerous due to the way they operated, being able to call on anybody for assistance, the Red Hood Gang, within a short time, began to rule over the city. Eventually the gang was targetted by an unknown vigilante, who later turned out to be the Batman, resulting in the collapse of the gang. The remaining members of the gang were then killed by the Joker.
Despite eventually collapsing, the gang still retained a huge legacy. Harley Quinn once adopted the Red Hood outfit simply out of the fact that the Joker was created due to the Red Hood Gang. Jason Todd also adopted the mantle of the Red Hood, using it for his mercenary purposes. It was the efforts of Todd that kept the Red Hood name alive and feared, though he used it for vigilante justice rather than mafia efforts.
Following the fall of the Red Hood Gang, a huge vacuum was created. Due to the decline of Falcone's Mob, this vacuum was filled by Penguin's Empire. However, the methods of the Empire were much more traditional than the radical efforts of the Red Hood Gang. Nonetheless, Oswald Cobblepot too would occassionally react to certain situations with the new form of crime.
The Red Hood Gang followed a unique style, allowing them to create a new form of gangster crime. Although the main Red Hood held a group of core followers, a majority of the Red Hoods were anything from ordinary citizens to homeless people to the wealthy. The main Red Hood was so feared that he literally owned the city, being able to call upon anybody he wanted at any time.