In the episode "There's No Place Like Home"(3x22), Captain Hook, also known as Killian Jones, reveals that he traded his ship for Emma in order to save her family. Following this confession, Emma kisses Killian and Captain Swan officially becomes canon.
Beginning in season 4, they start dating and hit huge milestones in their relationship, such as Killian revealing to Emma that she is his happy ending. Eventually, Emma admits to Killian that she loves him; however, this is moments before getting sucked into a vortex of darkness.
Their relationship progresses in season 5 where not only do they exchange the words "I love you" many times, but Killian also gives Emma Liam's ring, showing his devotion toward her. In another instance, Killian buys Emma a house that he hopes to share with Henry as a family. However, they don't get to have the "white picket fence life" they dreamed of as Killian makes the ultimate sacrifice for Emma, forcing her to kill him in order to save her and her family. Refusing to let her true love stay dead for long, Emma travels to the underworld to follow in the footsteps of her parents and split her heart in half, proving their true love and bringing Killian back to Storybrooke.
In season 6, even though their future is proved to be at stake when Emma learns that she's fated to die, they take the next step in their relationship. Killian proposes to her and she excitedly says yes. He assures her that no matter how uncertain her future is she can be certain that he will always be by her side. They get married, vowing to love each other for all eternity in front of all their friends and family.
In season 7, when they visit Emma's older son, Henry, who has since left home, Emma announces her and Killian are expecting their first child together, saying they are very happy together and excited to start this new adventure of parenthood together.
They first meet when Hook is undercover working for Cora. Emma and her group reach Safe Haven, only to find everyone has been massacred by Cora, save for one person--Hook. Pretending that he survived by playing dead, he gains the sympathy of Aurora. However, with her lie-detecting abilities, Emma is not fooled. When he won't reveal his true identity, Emma and her group tie him to a tree as ogre bait. Hook finally reveals himself and tells them he will turn on Cora and join their group if they can get him to Storybrooke, too.
Hook guides Emma and her team through Neverland, and he obviously has a crush on her, even telling her so. However, he is constantly rejected. Later, they kiss in "Good Form" (3x05). Though it was only of gratitude, it was extremely passionate.
They become friends after they return successfully from Neverland.
When Emma loses her memories, Hook tries to see if kissing her will trigger anything, but it doesn't. This was most likely since it was not a "kiss of true love."
After Emma gets her memories back, they become better friends. Zelena curses Hook's lips and tells him to kiss Emma as it will strip her of her newfound magic powers. However, he refuses to do so and instead represses his feelings for her. Realizing he will not kiss Emma without an impetus, Zelena drowns Hook. Though he is pulled form the water, he is unconscious. To save him, Emma is forced to give Hook CPR, and this mouth-to-mouth contact counts as a kiss, thus stripping Emma of her power.
When they are sent back in time together, they have several intimate scenes. In one instance, to distract the past Hook, Emma tries to seduce him. Slightly jealous, present Hook doubts it will work. However, Emma states that she is "exactly his type." After getting past Hook drunk, she offers to sleep with him, and he leads her to the Jolly Roger. They clumsily kiss as they make their way to the bedchambers. However, present Hook, who was on the ship as well, is jealous and knocks out past Hook.
After they return to Storybrooke, Emma learns that he sacrificed his ship for her. So, she kisses him of her own will.
In the beginning of season 4, Emma pulls away from Hook. Hook confronts her outside of Granny's in "Rocky Road"(4x03) and they have a tender moment, ending with a passionate kiss. Hook and Emma are now in a relationship.
In the season finale, "Operation Mongoose Part 2"(4x22), Emma reveals that she loves Hook to Regina after Hook is "killed" in an alternate universe, which was never really real. Later, Emma then is unable to tell Hook she loves him. However, moments before she sacrifices herself for Regina, she finally tells him before becoming the dark one.
When Emma becomes the dark one, she is transported to Camelot, so everyone travels there to save her. They meet up with Arthur, Guinevere, and Merlin. Merlin says he can take away Emma's darkness. However, he fails, and Hook is hurt badly.To save him, Emma turns him into the dark one, too. She creates a curse to bring everyone back to Storybrooke, and she takes away everyone's memories.
Soon, however, Zelena gives Hook back his memories and he is extremely angry at Emma. Emma does all she can to stop him from doing bad things, but she fails. Hook summons all the past dark ones from the Underworld. But at one point, as Nimue, a past dark one, is harming Emma, Hook comes to his senses and sucks all the dark ones back into Excalibur. So that all the darkness will be destroyed forever, he tells Emma to kill him. They share a kiss, and then Hook dies. Emma goes to see Rumpelstiltskin later and finds out the darkness was not destroyed but transferred back into Rumple. Enraged, Emma decides to go to the Underworld to bring Hook back.
Emma and Hook's love is confirmed to be true when the two try to use the True Love Scale. Emma chooses to save Hook instead of her own heart, allowing them to pass the test.
At the end of the season finale, "An Untold Story"(5x23), Emma decides to say those three little words, "I love you," to Killian without any battles or death between them.
During the first episode of the season, "The Savior"(6x01), Emma starts to get visions of what she thinks is her future. Worrying about what it may hold, she ponders her future with Killian. After establishing they have true love, Emma and Killian take the next step in their relationship, moving in together as of "The Other Shoe"(6x03).
In "Street Rats"(6x05), Emma opens up about her visions and tells everyone the truth. When he finds out, Killian tries to do everything in his power to prevent her destiny from being fulfilled, which results in him keeping a secret from Emma. Killian tells Emma the truth and she forgives him because she would have done the same thing.
Emma and Regina get stuck in a wish realm in "Wish You Were Here"(6x10), and Killian and David try to get them back to Storybrooke.
In "Murder Most Foul"(6x12), Hook confides to Archie that he wants to marry Emma as well as showing him the ring that he plans on giving her, but he doesn't think David approves of him. Archie tells Hook to talk to David about it. At the end of the episode, David gives Killian his blessing to marry Emma.
In "Ill-Boding Patterns"(6x13), Killian plans to tell Emma the truth. However, before he could say anything, Emma pulls out the ring that Killian planned on giving her and she says that there is nothing stopping them. Before he has the chance to tell Emma the truth, he gets down on one knee and asks her to marry him, and she says yes.
In "Page 23"(6x14), Hook tries to burn his memories of killing David's father, but Emma catches him in the act. She tells him that he should have told her about what he did. Until he starts to trust her, they should take a break. Killian goes to Captain Nemo for advice, but in doing so, Gideon traps him on the Nautilus with Nemo and his crew. Worrying where he disappeared off to, Emma goes to Snow and Regina in an attempt to take her mind off Killian.
Episodes later, during "Awake"(6x17), Emma and Killian are reunited and he proposes once again. However, this time, he does it the right way.
In the following episode, "Where Bluebirds Fly"(6x18), Emma is cooking pancakes in their kitchen while Killian sneaks behind her. He whispers in her ear "Something smells delicious," and Emma replies to that by saying "It's just from a box." To this, he replies "I'm not talking about the pancakes." Emma and Killian lock lips and Emma sits him on the edge of the kitchen table. They are about to deepen the kiss when Snow walks in on them.
In "The Song in Your Heart"(6x20), Killian and Emma finally exchange vows on a rooftop in Storybrooke. Less than ten seconds later, they break out into song! The final scene shows them holding onto each other as the dark curse draws nearer.
The curse alters Storybrooke, institutionalizing Emma and leaving only Henry and Gold "awake," while sending Emma's other allies to their original realms. The final battle begins over Emma's belief; if she stops believing in the realms of story, they will be consumed by the Darkness and cease to exist. To make matters worse, if all the realms are destroyed, Fiona will gain godlike powers and be able to break the Laws of Magic at will. Emma lays down her sword, allowing Gideon to impale her; this releases Emma's light magic and ends the battle, with both Emma and Gold having chosen good.
In season 7, Emma and Hook, now married, living happily, despite Emma's son Henry being away.
Several years have passed, and Henry is about to be captured by Lady Tremaine. Using the bottle, Henry calls Emma, Hook, and Regina so they can help him. Hook comes along with Regina, and the two succeed in saving him. However, unbeknownst to them, the bottle also brought over the Hook from the Wish Realm, who later appears and knocks the original Hook out to assume his place. When Emma arrives and reveals to Henry that she is pregnant, the other Hook feels guilty and decides to switch back. When a fight ensues, the real Hook ends up stabbing the other Hook. The other Hook then reveals that he had a daughter who got trapped in a tower by a witch. After hearing this, Hook gets Emma to heal his counterpart.
Happily married with an upcoming baby, Emma and Hook decide to return to Storybrooke and live there--their happily ever after.
Since Hook was first introduced, many "Oncers" have shipped Captain Swan due to their witty banter and common innuendos. In season 3, it became apparent that Hook had a crush on Emma, thus causing the CaptainSwan fandom to grow even more due to their sentimental moments and, more importantly, their first kiss in Neverland (even though Emma insisted it was a one-time thing). However, the ship had a rivalry with SwanFire. Many debated whether Emma should be with Neal since he was Henry's father. However, SwanFire petered out after Neal died. Soon, Captain Swan gained even more followers and became one of the most well-loved ships in the entire fandom.