Phoenix Force
The alias of Phoenix has been used by several fictional comic book characters published by Marvel Comics. The first, Baron Zemo, used the alias only once, but the later bearers of the identity are far more notable, and all are associated with the Phoenix Force. The Phoenix Force is famous for its central role in one of the most influential storylines in American superhero comics: the Dark Phoenix Saga.
The Phoenix Force is the nexus of all psionic energy which does, has, and ever will, exist in all realities of the multiverse. During its time as a sentient entity, it was known to possess the psyche of mortals (particularly those who happen to be telepaths) and thus amplify their psychic abilities to a cosmic (and in some cases, nearly incalculable) scale. Its primary form is that of a gigantic firebird.
Its known hosts have included Jean Grey and Rachel Summers, both members of the X-Men. Unlike the latter, the entity did not physically possess Jean Grey; instead, it created a second body identical to hers and through that body acted for her while she lay in a coma. However, the clone was created to mimic all aspects of humanity, including its flaws. Under the manipulation of such foes as Mastermind and Emma Frost, the Jean/Phoenix clone was unable to adapt to its newfound humanity and was driven mad; as Dark Phoenix, it destroyed a planet populated by sentient creatures and subsequently committed suicide. Jean Grey was later revealed to be alive, and later reassumed the name of Phoenix after marrying Cyclops.
Another person who went by the code-name Phoenix is Rachel Summers, Jean's daughter from an alternate future. She bears an uncanny resemblance to her mother.
Most recently, Jean began manifesting the attributes of the Phoenix Force. Despite this, she generally retained her self-control until her death at the hands of someone posing as Magneto.
Recently during the Marvel mini-series X-Men: Phoenix: Endsong, the Phoenix Force returned to Earth and resurrected Jean Grey from her grave. Through a number of incidents including Jean having Wolverine kill her a number of times, Jean trapping herself in a glacier, the Phoenix Force jumping into Emma Frost, and parts of the Astonishing/Uncanny X-Men teams being trapped in the Shi'ar event horizon, Jean Grey managed to assert herself and gain control of her Phoenix self and rescue everyone from the event horizon. As a result of the Shi'Ar's attack on the Phoenix Force, it is currently in an incomplete state. Jean is now searching for the remaining Phoenix fragments in order to make herself and the Force whole again.
Crossovers
Dark Phoenix teamed up with Darkseid in the Teen Titans/X-Men crossover between DC and Marvel Comics' respective teams. The story was made by Chris Claremont, Walt Simonson and Terry Austin in 1983. The story follows Darkseid conversing with Metron for the Anti-Life Equation at the edge of the Universe. Metron and Darkseid make a deal, and Dark Phoenix becomes part of that equation. The Teen Titans try to stop Darkseid, with the help of the X-Men who later go head to head with Deathstroke the Terminator. The Dark Phoenix breaks free from Darkseid's grasp.
The Phoenix Force was transported to the Ultraverse in The Phoenix Resurrection where it possessed the pyrokinetic ultra Amber Hunt. The X-Men, Ultraforce, Exiles, and numerous other characters team-up to stop the Phoenix from destroying the world.
Appearances in other media
The Phoenix has been seen in the X-Men 3 announcement trailer. Although it is currently not known what her role is, she is spotted walking alongside Magneto several times suggesting a possible opposition against the X-men.