The Fourth Reich's first mission was to kill the descendants of various patriotic American superheroes. Led by Vandal Savage, they struck hard, killing the Westons, the Thompsons, the Heywoods, and the then-current General Glory. However, they were ultimately stopped by the Justice Society. They're actions were responsible for the birth of Citizen Steel and the new Mr. America.
More recently, they have returned, using Obsidian to create a weapon called the Darkness Engine which negates everyone else's superpowers. Shots of them in the future imply that they will subsequently conquer the world.