Origin

Talia Al Ghul is the daughter of Ra’s Al Ghul. His father met her mother at Woodstock Festival, her mother was of Chinese and Arab descendant. After Talia was born, her mother overdosed on drugs and died. However, this part was quickly retconned. Her mother now was named Melisande and was murdered by one of Ra’s former servants. After the death of Talia’s mother, Ra’s took her traveling with him and taught her hand-to-hand combat. He also taught her how to use most the weapons in the world. When she grew older, she began to help him manage other parts of his organization.

Beloved

Talia and Batman

Talia meets Batman when he rescues her from Dr. Darkk who claimed to be the leader of the League of Assassins. Later it was revealed that Darkk was just one of Ra’s soldiers who failed a mission and attempted to take over the organization. Darkk would have Batman’s life in his hands, but is killed when Talia shoots him. In the classic story arc entitled “Daughter of the Demon,” Ra’s al Ghul finds his way into the Batcave and reveals that he already knows his secret identity. Ra’s then proceeds to ask help from Batman stating that both Talia and Robin had been kidnapped. Later it revealed that Talia had fallen in love with Batman, and this was all an elaborate plan by Ra’s to test Batman if he was a suitable heir. Batman declined Ra’s offer but returns Talia's feelings. In the years since Talia  and Batman have a stormy, on-again, off-again romance but she is repeatedly torn between loyalty to her father and her love of Batman. However, she has proven an important 'ally' in her way; most prominently, she encourages Batman to return to Gotham City when it is declared a "No Man's Land" following an earthquake, as he has lost his fighting spirit and didn't believe he could save Gotham.

Marriage 

Ra's al Ghul persuades Batman to join forces in their search for Qayin, a terrorist and rogue assassin. During this time Batman marries Talia and she becomes pregnant. After Batman's near death protecting her, Talia concludes that she can never keep Batman, as he will be continuously forced to defend her. She fakes a miscarriage, and the marriage is dissolved.

In reality, Talia gives birth to the child.

Jason Todd

When Jason Todd is resurrected, a stranger from his past, delivers him to Talia and Ra's Al Ghul , spending months in her care. But in order to revive him completely she throws him into the Lazarus Pit against her father's wishes. She helps him escape and informs him that his killer still lives.

Lexcorp

Talia began to reject her father’s ideals and plans for the world. She decided to leave him and his organization and began to temporarily run LexCorp while Luthor was the President of the United States. However, Talia was secretly leaking information to Superman in order to help him bring Luthor down. She also sold all of LexCorp’s assets to the Wayne Foundation.

Death of Maidens

Right before Infinite Crisis, Talia has become one of the core members of the Secret Society of Super Villains. It was later revealed that this was a plan by Nyssa to take over the world and bring it peace and equality. While Nyssa tries to recruit Cassandra Cain to join the League of Assassins, Cain declines, kills Nyssa, and takes over the League of Assassins.

One Year Later

After the death of Nyssa, Talia becomes the new Demon’s Head. However, Talia has lost control of the League of Assassins due to Cassandra Cain. Talia later makes an appearance and reintroduces her son from the Son of the Demon story arc and the father is supposedly Batman. His name is Damian and she leaves him with Batman in order to keep Batman busy while she unleashes an army of ninja man-bats to kidnap the British Prime Minister. Later Batman confronts Talia on top of a submarine with their son. Talia decides to shoot a torpedo towards them and Batman leaps off while Talia and her son stayed on. The torpedo exploded on the submarine but it has yet to be revealed whether Talia and her son survived or not.