Oligarchs were a secretive organization that the Machines identified as freeborn humans, although the Machines did not know their true intentions. The Oligarchs appear as glowing wireframe figures within the Matrix. Although it is revealed that they are humans, they no longer have bodies in the Real World and most of them have robotic bodies instead.
Due to their tremendous levels of system access they are able to override codes; enabling to do amazing feats: altering the physics around them. It is also almost impossible to attack them.