In Return of the Jedi (1983), Leia helps in the operation to rescue Han from the crime lord Jabba the Hutt and is revealed to be Vader's daughter and the twin sister of Luke Skywalker.
Darth Vader only learned he had a daughter in Return of the Jedi - but there's no evidence he realized she was Leia before his death and redemption.
Alderaan's princess knew she had been adopted by Bail and Breha Organa after the Clone Wars, but she had no idea who her parents were. That was until Luke Skywalker told her the truth - that he was the son of Darth Vader, and that she was his sister.
Darth Vader, in his previous identity as Anakin Skywalker, is a lead character in the prequel film trilogy and so is his wife and the twins' mother Padmé Amidala; while his mother Shmi is a minor character in the first and second films respectively.
He found out Leia was his daughter while fighting Luke in episode 6. He read Luke's mind during the fight and discovered that Luke had a sister. He was trying to find a weakness in Luke and discovered that he was worried about the safety of his sister.
However, Leia's strong-mindedness during Vader's probe denied him the opportunity to discover that she was his daughter. This serves to justify Vader's lack of awareness of his connection to Leia, although perhaps not as satisfyingly as if Lucas had planned for the relationship from the beginning.
Attended by medical droids, Padmé Amidala gave birth to her twins Luke and Leia on Polis Massa. She died and the twins were split up, with Obi-Wan taking Luke to Tatooine and Bail Organa returning home to Alderaan with Leia.
In The Phantom Menace, when Qui-Gon Jinn meets tiny Anakin Skywalker and his mother, he goes on about how the Force is like, crazy strong with Anakin or whatever, and then asks his mother about Anakin's dad. Shmi Skywalker is pretty clear in her answer: There isn't a father. She was impregnated by the Force.
Leia married Han Solo in 8 ABY and had three children: twins Jaina and Jacen in 9 ABY, and a younger son Anakin, who was named after his grandfather, in 10.5 ABY. In 19 ABY, Luke married Mara Jade. Their son, Ben, who was named after Luke's first mentor Obi-Wan "Ben" Kenobi, was born in 26.5 ABY.
Rey (portrayed by Daisy Ridley) is the granddaughter of Sheev Palpatine/Darth Sidious through Dathan. Born on the planet Hyperkarn in 15 ABY, as a child in 21 ABY, Rey was abandoned by her parents on the planet Jakku to protect her from Sidious.
In the rough draft of Star Wars: Episode IV A New Hope, Darth Vader tortures Princess Leia with powerful electroshocks. In the incarnation of the second draft of A New Hope, Leia is replaced by Deak Starkiller, the brother of Luke Starkiller (who would become Luke Skywalker in later drafts).
It's well known that Star Wars lead characters Luke Skywalker and Princess (now General) Leia are brother and sister. The estranged siblings didn't know about their familial relationship until "Return of the Jedi." They even shared a passionate kiss in the previous movie, "The Empire Strikes Back."
First excerpt from The Princess and the Scoundrel features Luke telling Leia about Anakin's redemption after Return of the Jedi. In Return of the Jedi, Luke Skywalker reveals to Leia Organa that they are siblings, and that Darth Vader is their father.
In 2 BBY, Leia was captured by crime lords during a relief mission and turned into a slave girl. During her imprisonment she was raped and impregnated with her son, Liam, who, despite the circumstances of his birth, Leia loved her son.
He only senses Luke when he actually using the Force, Leia is not actively aware or using the Force and therefore he does not sense her. He is also not looking for a daughter either until Luke spills the psychic beans on her later on.
After years of speculation, Star Wars: The Last Jedi revealed that Rey (Daisy Ridley), the main character of the new trilogy, is not the child of Luke Skywalker (Mark Hamill). In fact, she's the child of “nobody” — per Rey's own words.
After The Empire Strikes Back, Han and Leia do continue their relationship. In Episode VI, Han is nearly ready to distance himself from Leia since he thinks that Leia and Luke are into each other. But once Leia reveals that Luke is her brother, Leia rejoices and kisses Han, making them a couple for good.
Their son Ben turning to the dark side and becoming Kylo Ren was the ultimate reason for the separation, but an excerpt from an upcoming Star Wars book indicates their relationship had issues that couldn't have been resolved.
Senator Padmé Amidala of the planet Naboo became pregnant during the Clone Wars with her husband, Jedi Knight Anakin Skywalker, as the father. She gave birth to twins, Luke Skywalker and Leia Organa.
In the canon comic Darth Vader No. 25, it is revealed that Palpatine somehow used the Force to manipulate midichlorions to impregnate Shmi Skywalker.
After death, Padmé became the mother-in-law of Han Solo and the maternal grandmother of Ben Solo/Kylo Ren. In the Legends, Padmé had four grandchildren, Leia's and Han's children: Jaina, Jacen, and Anakin and Luke's son, Ben, and mother-in-law of Mara Jade Skywalker.
After her death in childbirth on Polis Massa, Amidala's body was returned to Naboo for the proper funeral rites. In order to hide the fact that Amidala's twins survived, her body was prepared to still appear pregnant.
At the end of the war, Bail Organa adopted Padmé's daughter Leia and raised her as an Alderaanian princess.