Leia initially had a rocky relationship with Han - due to Han being a greedy and selfish smuggler at the time. During their escape from the first Death Star, she became extremely annoyed by Han's recklessness, as he placed them at risk and almost got them captured several times. During the Battle of Yavin, however, when Vader almost succeeds in killing Luke - Han saved him - after this Leia's opinion of Han changed - and they slowly fell in love with each other. Leia and Han developed a relationship that would last throughout the war.
In The Empire Strikes, Leia did not admit she had romantic feelings for Han at first. However, after they were captured by the Empire; moments before Han became frozen in carbonite, Leia realized that she loved him and admitted her romantic feelings for him.
In Return of the Jedi, Leia, along with Luke, Chewbacca and Lando Calrissian go to Tatooine to rescue Han from Jabba the Hutt; their rescue mission is successful and Leia and Han lovingly embrace each other.
After Luke revealed that not only is Vader his father but hers as well, that he is her older twin brother, and left to be captured by the Empire - Han appeared to question Leia about the relationship between her and Luke, (unaware of what their conversation was about). Leia was initially unable to tell him, as she was still in shock to find out that Vader was her father and Han became jealous of Luke, but soon apologized and comforted her.
In the aftermath of the Battle of Endor, Han reassured Leia that Luke had surely survived; that he had got off the second Death Star, before it was destroyed, but she already knew it, as she felt her brother's presence though the Force. Han told her he would not interfere in their relationship, but Leia informed Han that Luke is her brother, much to his shock and and embarrassment, and they subsequently share a passionate kiss.
Sometime after the Battle of Endor, Leia and Han married and had a son named Ben, however, when their son fall to the Dark side, becoming known as Kylo Ren, they separated for years in agony and grief, each moarning the loss of their son in their own way.
In The Force Awakens, after not seeing each other for many years - Leia and Han are happily reunited. Before going with Chewbacca and Finn, to rescue Rey and destroy the Starkiller Base, Leia and Han lovingly embrace each other (unknown to either of them, this would be the last time Leia would see Han alive). Upon Han's murder at the hand of their son; Leia senses Han's death through the Force, and, devastated by the death of her husband - she mourns his loss and blames herself for his death.
Leia did not meet her father until nineteen years after she was born. By the time she met him on the Death Star, the encounter with her father was a cruel twist of fate, both Leia and Vader were unaware of there relationship with each other at the time. Vader treated her as an enemy to the Empire and severely tortured her aboard the Death Star for information regarding the location of the rebel base - all before letting Wilhuff Tarkin destroy her surrogate home; Alderaan.
Leia (incorrectly) saw Vader as a monster willing to destroy the weak. However, she became shocked upon learning of her true relationship with Vader from Luke - that Vader was in fact, her father. She likely had mixed feelings for her father after this discovery; until learning of Anakin's ultimate sacrifice to save her brother's life, Leia now realizes that her father was never the monster she believed him to be, and all her beliefs about him were wrong, it is very likely that she now has great respect for Anakin.
After she is born, unlike Luke, Leia never had any direct interaction with Padmé, however, due to her immense strength in the Force, Leia was left with a lasting impression of images and feelings of her mother - that she was "very beautiful, kind, but sad".
After Padme's death, Bail took Leia in and raised her to devoted her life to overthrowing the Emperor and restoring the Republic he had destroyed but to keep this part of herself to herself so their people don't get in trouble.
After Bail was killed when the Alderaan system was as destroyed by the first Death Star, as Bail was on the planet Alderaan; when it was destroyed, Leia grieves over the death of her adopted father.
Leia and Luke were separated after they were born, she did not meet her older twin brother until nineteen years later. Luke, along with Han Solo rescued her from the first Death Star; after Luke becomes a member of the Rebel Alliance, the two became close friends.
In The Empire Strikes, Leia only considers Luke a friend, however, she kissed him in a failed attempt to prove she doesn't have any romantic feelings for Han; much to Luke's annoyance.
In Return of the Jedi, Luke revealed to Leia that Vader was his father and she - his twin sister. Leia is not overly surprised as there was always a part of her that suspected the relationship between herself and Luke. After the second Death Star - Luke joins the rebels in their ultimate victory against the Empire. Leia and Luke lovingly embrace each other as brother and sister.
Not much is known about her relationship with her son and only child; however, Leia likely had a loving relationship with her son. Prior to Ben's fall to the dark side - when her son started to struggle with the Dark side of the Force - Leia was terrified that he might end up like his maternal grandfather Anakin Skywalker and so - sent him to study under the tutelage of her brother, Luke.
Unfortunately - Luke was not able to prevent Leia's son from falling to the Dark side - as Snoke preyed on Ben's internal conflict. Ben, upon conversion to the Dark side, became known as Kylo Ren. Leia was devastated that her son had become evil and moarned him bitterly, yet, despite the atrocities that Ren had committed over the years - Leia still believed that Ben could come back to the light and be redeemed.
Friends and Allies
Leia never officially met Obi-Wan, but had heard a lot about the Jedi Master from her adopted father, Bail Organa, moments before she was captured by the Empire, Leia gave the secret technical plans of the Death Star, to R2-D2 as well as a message for Obi-Wan; she sent the astromech droid to find the Jedi Master; to recruit him into the Rebellion.
After Obi-Wan was killed by Darth Vader, she was upset over his death, Leia apparently named only son and child after Obi-Wan, albeit after his alias; "Ben Kenobi", despite the fact that she never personal known the elderly Jedi Master.
Leia didn't trust Lando at all when she first met him. Her doubts were apparently justified when he helped Vader capture Leia and her friends (unaware that he only did this; because Vader, under the orders of Palpatine, threatening to take over Cloud City if he didn't help them). Leia forgave him after she learned why Lando did it, especially after he helped rescue Han.
Unlike her father, Anakin Skywalker, Leia hated Palpatine from an early age; Bail raised her to be dedicated to overthrowing Palpatine and restoring the Republic he had destroyed. He also taught her to keep these sentiments to herself so Alderaan would not get into trouble. When Leia was discovered to be a Rebel - Palpatine used her allegiance as a pretext to do what he had always intended - to dissolve the Imperial Senate permanently and destroy what was left of the Old Republic's bureaucracy - making himself an absolute monarch.
Leia and Tarkin did not have much interaction with each other, however, when she refused to give the location of the rebel base - he threatened to destroy her home planet Alderaan. When Leia apparently did reluctantly provide the location of the rebel base - Tarkin went back on his word and destroyed her home planet anyway. However, it was later revealed that the location she gave them; (Dantooine), was a rebel base that had been abandoned for some time. She had mislead them, knowing that if the rebellion had fallen, the Empire's tyranny would continue and she also did not believe Tarkin would keep his word. Leia was disgusted by what Tarkin had done - as Alderaan was completely innocent and was not even a part of the rebellion.