The X-Men are a team of superheroes made of up of mutants (Homo Superior). It's a team which has been around for decades, fighting to have mutants accepted by normal humans. They've defended humans from mutant supremacists, terrorists, killers, and criminals and have defended mutants from those humans who would enslave, sterilize, or exterminate mutantkind. The X-Men also defend Earth from both extra-dimensional and alien threats. At times it has consisted of only one team and at other times multiple teams.
Which have operated on Earth, the Moon, elsewhere in the Milky Way galaxy, neighboring galaxies (Andromeda, Shi'ar, etc), and other dimensions. Some of its members have traveled to the future or the past, or even other realities. The team has clashed with gods, demons, aliens, and governments. Some of its members have been involved in universal scale events. Recently they along with most of the world's mutants have migrated to the sentient living island of Krakoa, establishing a mutant nation.
It's a team which has had a long history of conflict with the demonic N'Garai due to the dimensional barriers being weak in the area where the Xavier Mansion is located. N'Garai Cairn periodically appear on their grounds resulting in N'Garai attacking the X-Men. In their most recent clash with the N'Garai, it was a global battle, as N'Garai cairns were appearing in multiple locations around the world.
Several members of the X-Men encountered Quoggoth, the rebellious creation of Shuma-Gorath, at Magneto's island and later when the X-Men temporarily based themselves on the island they found themselves in combat with the reactivated ancient eldritch defenses. Once the X-Men found themselves trapped in a New York City where the reality altering magic of Kulan Gath a sorcerer and high priest of Shuma-Gorath had turned it into a Hyborian city in which all of its inhabitants (except Spider-Man who somehow was immune) believed themselves to be living in the Hyborian Age.