The X-Men is a group of mutants founded by Professor Charles Xavier.
Wolverine and the X-Men Edit
The Professor found each of the X-Men and invited them to join his school for mutants. They all did so, and became much like a family. However, in the pilot episode of Wolverine and the X-Men, Jean's Phoenix power exploded, causing Professor Xavier to be sent to twenty years in the future. In the future, Xavier learns of the events that will cause the apocalyptic future and tells the X-Men how to solve them.
The X-Men are located in the X-Mansion, which they all refer to as 'The Mansion'. It was destroyed in the blast shown in the pilot, but since has been rebuilt thanks to Angel.