Golden Age
The original Hawkman's story actually begins in the days of ancient Egypt, when he was known as Prince Khufu. For years, his bitter rival was the priest Hath-Set. One day Hath-Set got the upper hand, and captured both Khufu and his lover, Chay-Ara, and murdered them both using a cursed dagger made on an alien substance called Nth metal, later revealed to be from the planet Thanagar. This Nth metal which killed them began a cycle of endless reincarnation for all three individuals. Eventually, in the early 20th Century, Khufu is reincarnated as American archaeologist Carter Hall, and Chay-Ara as Shiera Saunders. Hath-Set was reborn as scientist Anton Hastor.
When Carter Hall discovered the Nth Metal dagger used to kill him in his previous existence, he touches it and instantly recalls all of his former lives. Hastor, reliving his own past as Hath-Set, then kidnaps Shiera, hoping to murder the pair all over again. Hall, now equipped with lost knowledge, creates a gravity-defying belt using Nth metal and a pair of wings to help him maneuver himself in the air, and becomes the Super-Hero known as Hawkman. Carter rescues Shiera, and Carter and Saunders become a romantic couple. She soon becomes his partner in fighting crime, calling herself Hawkgirl.
Hawkman becomes a charter member of the Justice Society of America, and later the wartime All-Star Squadron. Eventually, Hawkman even became the team chairman. But as the war ended and the 1940s became the 1950s, the Justice Society of America disbanded, and Hawkman and Hawkgirl retired from heroics for a time. They married, and had a son named Hector, who would grow up to become the hero called Silver Scarab, and later, Doctor Fate. The adventures of the Golden Age Hawkman and Hawkgirl originally took place on the world designated Earth-Two within the Multiverse. But on its counterpart Earth-One, a new and different Hawkman would soon emerge.
Silver Age
On the distant world of Thanagar, police officer Katar Hol was one of his homeworld's most respected and decorated officers. On this planet, the police wore anti-gravity belts and their wings, very similar to what Carter Hall used on Earth-Two. These were inventions of Katar Hol's father, Paran Katar. Katar Hol's wife, Shayera, was also a police officer, as well as Katar's partner. Eventually, the two were sent to Earth to apprehend the man called Byth, who was a criminal shapeshifter. Once he was captured, the two heroes decided to stay behind on Earth, in an effort to learn human police methods.
On Earth, they took on the human aliases of Carter and Shiera Hall, and became the Super-Heroes Hawkman and Hawkgirl. As part of their new identities, Carter and Shiera became museum curators in Midway City. Hawkman soon joined the newly formed Justice League of America. Although he and his wife both had advanced alien tech at their disposal, the Hawks also liked using the ancient weaponry found in their museum during battle. Hawkman and Hawkgirl (later Hawkwoman) were among Earth's most respected Super-Heroes for years. As a member of the League, Hawkman became close friends with the Atom, although he often got into heated ideological arguments with his teammate Green Arrow. When the JLA and the JSA crossed dimensions, he was able to meet his Earth-Two doppelganger, also named Carter Hall.
Bronze Age
Eventually, Hawkman discovered that his people the Thanagarians were involved in a war against the planet Rann, home of fellow hero Adam Strange. Because he opposed this war, and publicly sided against his own planet, he and Shayera were subsequently exiled, and the planet that was supposed to be his temporary home became his permanent one. It was during this time that Shayera changed her name from Hawkgirl to Hawkwoman, and joined her husband as a member of the Justice League. Sometime later, Hawkman discovered that the Thanagarians were plotting a stealth takeover of Earth, and fought them in what he referred to as his "shadow war." Eventually, Thanagar gave up their plans to dominate Earth thanks to Hawkman's interference.
Post Crisis
After the events of 1985-1986's CRISIS ON INFINITE EARTHS, the Multiverse was reshaped as one universe. The histories of Earth-One and Earth-Two were merged. The Golden Age Hawkman Carter Hall now served on both the Justice Society and later, the Justice League, providing a connective tissue between both teams. After the Crisis, Carter and his JSA compatriots disappeared into another dimension in order to prevent Ragnarok from taking place on Earth. A "Hawkman" named Fel Andar would take his place briefly in the Justice League International pretending to be Carter, but he was eventually exposed as an imposter and Thanagarian spy. But not long after, a new version of Katar Hol would come to Earth and become the new Hawkman.
The Post-Crisis Katar Hol was a young Thanagarian police officer, the child of a wealthy family whose patriarch, Paran Katar, was the inventor of the hawk wings. Thanagar was now a conquering world, one which subjugated other planets and strip minded them of their resources so the natives could live in luxury. Katar hated what his world had become, and would lose himself in the past by studying his planet's history. During this time, a disillusioned Hol became a drug addict, and was manipulated by corrupt police captain Byth into killing his own father, and was then sent into exile.
After recovering from his addiction, he returned from his exile and was reinstated into the police force, but sent to the planet's dangerous "Downside," where crime was rampant. He was eventually able to expose Byth as the man who engineered his father's death, and cleared his name. Now partnered with a woman named Shayera Thal, both Katar and Shayera were sent to Earth as goodwill ambassadors, where they became the new Hawkman and Hawkwoman.
When original Hawkman Carter Hall returned from his other-dimensional exile to stop the coming Ragnarok, he met his namesake, and revealed that he actually knew his father Paran Katar, who had journeyed to Earth during World War II. It was Carter's Hawkman persona which inspired Paran to invent what would become the Thanagarian police force. Carter also revealed that Paran had met a Cherokee shaman named Naomi whom he fell in love with, and the two married with Carter and Shiera as witnesses. She gave birth to Katar, thus making him a human-Thanagarian hybrid.
During the crisis in time known as the Zero Hour, Carter Hall and Katar Hol, along with Shiera, merged into one mystical being called the Hawk-God avatar. Although the Hawk-God fought injustice for a time, the voices in his head of the different people he was comprised of ultimately drove him insane. The Carter Hall aspect of him would eventually break free into a new and younger body, thereby rendering the Katar Hol aspect of him dead. This new, younger Carter Hall however would retain some of Katar's memories, and his physical body looked more like Katar Hol. He rejoined the newly re-formed Justice Society of America. Shiera was reborn too, as Kendra Saunders, but unlike Carter, she had no memory of their past lives together. They became crime-fighting partners in St. Roch, Louisiana, but Kendra resisted becoming romantically entangled with Hawkman.
Post Infinite Crisis
In the events leading up to the cosmic upheaval known as 2006's INFINITE CRISIS, Carter Hall becomes the chairman of the JSA for a time. But poor judgment leads to several people being killed during his leadership. He leaves Earth to contemplate his mistakes, and allows Hawkgirl to become Earth's resident winged warrior. He eventually returns to Earth, where he and Kendra team up again as Hawkman and Hawkgirl. But their reunion is short-lived, as the Black Lantern versions of Elongated Man and his wife Sue murder the Hawks in cold blood at the dawn of the Blackest Night, thus transforming their corpses into new members of the Black Lantern Corps.
Luckily, during the final battle of the Blackest Night, Hawkman and Hawkgirl are both resurrected by the power of the White Light of life. Kendra is now reborn as Shiera Hall, and now she remembers all her past lives, and she and Carter finally truly reunite as a couple. But yet another cosmic upheaval in the Multiverse would soon change the lives of the Hawks all over again.
New 52
After the events of 2011's FLASHPOINT, reality was altered, and a new Hawkman would appear on Earth, this one a new version of Katar Hol of Thanagar. Although at first this "Savage Hawkman" seemed to have no memory of being an alien, he soon discovered that he was really a member of the Thanagarian race, who in this reality had natural wings. He was a popular gladiator who became the adopted son of King Thal Provis, as well as the consort of the King's daughter, princess Shayera Thal. Katar was unique among his people as he was a pacifist, and used his sway with the king to have him hold a peace conference with their enemies. However their enemies saw the peace conference as an opportunity to strike, and used it to kill King Provis.
The new ruler, son of Provis and Katar's adoptive brother, Corsar, believed that only the powerful Nth Metal could save them from their enemies, but this actually ended up killing hundreds of Thanagarians. Katar was accidentally fused with it creating a full body armor and regenerating his wings. But seeing that his adopted brother was becoming a madman, and refusing to see the danger in the Nth metal, Katar refused to let the metal power be distributed. This lead to a battle between himself and his adopted brother, which lead to the death of Corsar. Shayera makes a vow to hunt down Katar, as she also sees him as responsible for her father's death. He runs away in a stolen ship that ends up crashing on Earth, where he seemingly loses his memory.
When his ship was found by the Coast Guard, they asked for his name, and he said "Katar Hol" before going unconscious. They misunderstood him, believing he said his name was "Carter Hall". The US government then gave papers and a new identity to Katar Hol, and he went on to college to study archaeology, and he becomes an archeologist in due time. He ends up joining the government sanctioned Justice League of America for a brief stint. Eventually, he returns to his homeworld Thanagar, which he saves from the alien despot Despero, but he himself dies heroically doing so.
Rebirth
Due to the events of 2016's DC UNIVERSE REBIRTH SPECIAL #1, the history of Earth was altered yet again. The original Hawkman, Carter Hall, returned once more. He was once again an archaeologist, one who was trying to figure out the secret behind the mysterious Nth Metal. He was always trying to unlock the mystery of his eternal loop of endless reincarnation, and he began to have nightmares of what later turned out to be the Dark Multiverse. Carter learns that his reincarnations have been not only across time, but also space, and in one of these incarnations he was Katar Hol of Thanagar. Since he would have technically coexisted alongside the post-FLASHPOINT Katar Hol, it is unknown if he was wiped from existence, or is somehow a part of Carter.
Two decades after the original Hawkman was introduced, a new version came on the scene. Decked in a very similar costume to the original, this Hawkman was the alien police officer Katar Hol. In his first Silver Age story, we see Hawkman and his wife come to Earth to capture the criminal shapeshifter named Byth. Deciding to stay on Earth to study human police methods, he and his wife Shayera becoming Earth's latest alien crime fighters. 
homeworld of Thanagar and its strict class system, as well as his troubled relationship with his father. He also met his new partner in the Thanagarian Wingmen, Shayera Thal. He sported a severe, armored look in this incarnation, as well as featherless metal wings.
When the Justice Society of America reforms in the 21st Century, the original Hawkman returns once more. Having been fused into a Hawk-God with Katar Hol years before, JSA member Hawkgirl (Kendra Saunders) found herself on war-torn Thanagar, where the high priests were hoping to use her special connection to Carter Hall to bring him back and stop the conqueror Onimar Synn from taking over their world. Using Kendra's soul connection, they brought back Hawkman to this plane of existence. He rejoined the JSA in this storyline.
In the post-FLASHPOINT universe, all previous Hawkmen seem to have been erased from history. A new Hawkman appears, going by the name of Carter Hall. He wears deadlier weapons on his gauntlets than previous versions, and is far more savage in battle than the Hawkmen of the past. Although he is named Carter, it revealed that he is really Katar Hol from Thanagar, although at first he seems to have no memory of his previous life before arriving on Earth. Eventually, his true alien nature would be revealed to him.