As the founder and captain of the Straw Hat Pirates, he is the first member that makes up the crew as well as one of its top three fighters. Luffy was one of eleven rookie pirates who had been referred to as "The Eleven Supernovas", the eleven pirates with bounties over
Luffy has a worldwide reputation for causing trouble, even among the Shichibukai and the Marines, committing crimes against - as well as actions that were deemed threatening by - the World Government.
He has gained a reputation for being 'reckless' and, in some cases, 'insane', after causing an incident in Enies Lobby, entering and escaping Impel Down, and joining the Battle of Marineford. He is therefore famous for being the only pirate to not only break into the three most important government facilities, but also escape from all of them alive.
This, plus the fact that he punched out a Tenryubito with full knowledge of the consequences and his heritage has caused Luffy to be labeled as a "dangerous future element".