The Birth: Jean Grey was the first student of Charles Francis Xavier and she made her starring debut in X-Men (vol.1) #1 (September 1963). She first manifested her powers during an accident with a friend of hers. While playing frisbee with Annie Richardson, this girl ran to get the disk and got caught by a car. Trying to calm down her friend, Jean began to talk with her and entered her mind, using her telepathic powers. She remained with Annie until she died, entering a coma that no doctor could heal. She was taken to the Milbulry Institute, owned by Mr. Sinister. Since these early days, Essex saw the potential that laid on young Ms. Grey. But he couldnīt handle her coma either. Only when Professor Xavier talked to Professor Grey, Jeanīs father, about his skills, the girl had a chance to live again. Working in secret, Xavier used his telepathic powers to take Jean from the dark side of her own mind, and blocking her dormant telepathic powers so they couldnīt harm her until she had complete control over them. Jean became a student of the Professor for some time, until getting back to a normal life.

The Alter Ego: Jean has spent most of her life with the X-Men. She had an initial crush on her teammate, Angel. But soon she fell in love with young Scott Summers a.k.a Cyclops; the leader of the X-Men. After the Krakoa incident she met Wolverine; then a new recruit. The two of them developed feelings for each other, feeelings that confused Jean about both Wolverine and Scott. But later, she went back to Scott and much later; after she returned from her second ressurection; married Scott. For a while after the Krakoa incident, Jean left the group and pursued a career as a designer. Jean also had a girlchild called Rachael Summers.

The Legend: When Professor Xavier started to form his group of mutants called the X-Men; Jean was by then a teen had already begun to realize her telekinetic powers; took the name of Marvel Girl and joined the group. It was during this time that she met Scott Summers and fell in love with him.
Much later, when the group was sent out to search for a mutant on the island of Krakoa they were all captured by the island itself. Only Scott escaped. Xavier recruited a new group of mutants to free his team and among them included Wolverine. Jean got confused about her feelings for Wolverine. She left the team for a short time but soon returned to Scott and the team.
In her first adventure after her return, she was captured by Steven Lang and his Sentinels, and taken to a S.H.I.E.L.D. base in space. The rest of the team saved her, but to get out of the place, they had to use a damaged space shuttle. Jean used her telekinetic powers to keep the radiation out of the ship and control it to Earth. But her powers were not enough to do it. The solar radiation that was surrounding the area was in fact a cosmic entity, the Phoenix Force, that seeing Jeanīs efforts to live and to save her friends, protected her, taking her memories and shape. The Phoenix "became" Jean, and put her to recover in the bottom of Jamaica Bay, in a protective cocoon. The ship crashed in the bay and Jean resurfaced moments later as Phoenix, her costume changed and her powers much stronger. The rest of the team believed her love for Scott and latent power had resurrected her from the dead, and so it seemed.
As time passed, the X-Men became more and more fearful for Jean. The power had begun to consume Jean, her mortal vessel unable to contain such a cosmic force and keep it under control. when the Hellfire Club began to use Master Mindīs powers to control the Phoenix so she could be their Black Queen, the entity got mad. Eventually, she lost control completely, becoming Dark Phoenix, an evil version of herself.
Phoenix shut down Wyngardeīs mind and left for space. She destroyed the sun of the DīBarin solar system and then returned to Earth. Unfortunately, the system the sun supported was inhabited, and the creatures living in it were consumed in the supernova she created. None of the X-Men were aware of what had occurred, and Jean, for her part was battling the darker side of herself, switching back and forth between personas. But while the X-Men were unaware of the crime there were people in space who were not. The the Shi'ar came calling, demanding that the price for the innocent lives she had claimed was her own life in exchange. The X-Men saved the Phoenix, but the entity sacrificed herself so it would never revert to itīs Dark Phoenix form. Cyclops almost died in this moment of suffering and left the X-Men for the first time. He, soon after, met Madelyne Pryor, the exact copy of Jean Grey and married her.
The X-Men thought Jean dead for many years, until the Avengers made an amazing discovery at the bottom of Jamaica Bay. They had found a cocoon which they were unable to penetrate, and called Reed Richards of the Fantastic 4 to research it. Inside, Richards found a woman, perfectly preserved, and looking like Jean Grey. He in turn, called Cyclops who left immediately to discover whether or not it was, in fact, Jean. It was indeed. And with her second resurrection, a new team was born. X-Factor brought together the original members of the X-Men once again, and Jean kept her original name of Marvel Girl.
When Jean Grey was believed to be dead, the villain Mr. Sinister had cloned a duplicate of her for his own schemes, no longer having access to the original. The clone was perfect, but without the soul to give it life. In the instant the Phoenix had sacrificed its vessel to save the universe, it tried to return to Jean Grey the portion of herself it had taken from her. But that portion was now soiled with the blood of the lives the Phoenix had taken, and Jean Grey rejected it. Having nowhere else to go, the Phoenix found the clone of Jean Grey, and deposited the portion it held of her into the lifeless body. This clone was to be Madelyne Pryor, wife of Cyclops.
Madelyne became insane when Sinisterīs Marauders kidnapped her son. She then allied with the demon Nastyrth to get powers and to save her kid. Madelyne now had demon-like powers, plus telepathic and telekinetic ones. Finding Sinister, she discovered her sonīs whereabouts and her true origin: she was a clone of Jean Grey, made from a cell that Sinister took from Jean during her days in the Milbury Institute. During the Inferno Saga, Jean, Scott, X-Factor, X-Men and New Mutants fought Madelyneīs forces. Jean discovered that the Phoenix, after "killing" itself in the moon in the fight against the Imperial Guard, tried to return to Jean and give her memories back. As Jean rejected her, the Phoenix went for Madelyne, who was ready in Sinisterīs lab, coming back to life. In the end of the battle against Madelyne, Jean absorbed her and the portion of the Phoenix Force that laid inside her, having 3 identities inside her mind. Accepting this portion, Jean became whole again and Madelyne passed from the world.
Some time later, Jean Grey met Rachel Summers, who claimed to be her daughter from another timeline. Jean rejected her at first, but began to have a mother/old sister relation with her after. By this time Scott had asked her in marriage, but the memories of Madelyne inside her made Jean say no. After the attack of Apocalypse to Cyclopīs son, and the battle against the Shadow King, Jean and the members of X-Factor returned to the X-Men.
Eventually Scott and Jean were married. They spent their honeymoon raising Scott and Madelyne's son in an alternate timline. After several years there, they were returned to Earth. Jean went without a moniker for a long time before finally deciding to take back the name Phoenix.
The X-Men later had to deal with the problem of Onslaught entity took her to the astral plane, revealing Xavierīs love for her. She with other heroes fought and defeated Onslaught, a battle which claimed the lives of the Avengers and the Fantastic Four. With their sacrifice, the entire responsibility of protecting the earth fell onto the shoulders of the X-Men's leader; Cyclops - this heavy responsibility was eased by Jean's love for Cyclops.
Soon after, Jean lost her powers, thanks to psionic wave that the Shadow King released in the astral plane.
While Jean Grey has a normal human beings strength, she had been trained in hand-to-hand combat by Wolverine. She also heavily relies on her psionic powers in combat. Telepathy enables her to read minds, project her thoughts into others' minds and stun the minds of others with "mental bolts". Telekinesis enables her to levitate herself, other living beings, and objects.

X-Men #1