The Gorosei (literally meaning “Five Elder Stars”) are the heads of the World Government, and as such, they essentially rule the entire world. They are the five men who rule above the Marines, Cipher Pol, and the ones who made a pact with the Shichibukai. So far, none of their names have been revealed.
The tall thin one with the mustache (second from right) spoke with Professor Clover and ordered Spandine to kill him before the archaeologist could speak the Great Kingdom’s name. They have shown to have at least a basic knowledge of the occurrences of the Void Century, according to their shocked reactions to Professor Clover’s statements. They have shown a paranoid fear of someone reviving the ancient weapons, to the point of forbidding its research and ordering the utter destruction of the entire country of Ohara, though given what is known of the Void Century, they may simply be using that as an excuse in order to prevent information they do not want leaked to the public from getting out. Despite this, they are not completely heartless, as they were hesitant about ordering the destruction of Ohara.