Zutara

Zutara is a Het ship between Zuko and Katara in the Avatar: The Last Airbender series.

Canon
Zuko and Katara were initially enemies because Katara was working with the Avatar Aang while Zuko was trying to capture him so that he could regain his honor and return home from his banishment. Despite this, Zuko never harbored ill feelings towards Katara for trying to protect Aang. In fact, he tried to reason with her and explained that he just wanted Aang so that he could go home. The two later fought at the Northern Water Tribe when Aang was in the Spirit World and Zuko tried to capture him.

At some point, Zuko and his uncle became wanted by the Fire Nation so they had to travel as refugees. Azula shot Iroh with lightning and Katara tried to go help him and Zuko with her healing but the latter was panicking and scared Katara off. Later, Katara and Zuko were both imprisoned together underground in Ba Sing Se. Katara yelled at Zuko and cried about losing her mother to the Fire Nation. Zuko then revealed that he also lost his mother to the Fire Nation and sympathized with her. Katara eventually offered to heal Zuko's scar with her spirit water but they were interrupted when Aang and Iroh arrived to save them. Azula offered to let Zuko return home if he fought against Team Avatar so he turned on them and Iroh. Katara was very hurt by this because she thought that Zuko had changed.

After being at home in the Fire Nation, Zuko eventually came to his senses and decided to join Team Avatar so that he could teach Aang firebending. Nobody trusted him at first and Katara was strongly against adding Zuko to their group. Even when he earned the trust of everybody else, Katara was still skeptical and threatened to kill him if he took even one step backwards. Zuko was upset that Katara did not trust him so he eventually helped Katara find the man who killed her mother so that she could confront him. Katara finally forgave him afterwards and hugged him.

Katara and Zuko were on much better terms and even sat next to each other when watching a play about themselves. While watching the actor of Zuko calling Iroh stupid, Katara asked if he really said that and Zuko lamented that he might as well have. Eventually, Aang went missing so the group found Iroh and he assured them that Aang would face Ozai. Katara decided to join Zuko in his battle against Azula. She eventually shot lightning at Katara so Zuko jumped in the way and took the shot. Katara managed to finish the battle and beet Azula. She then went to heal Zuko while crying but succeeded. Katara comforted Zuko while he was watching Azula go insane. She later attended Zuko's coronation as Fire Lord and was smiling.

Fanon
Zutara is one of the most popular ships in the Avatar: The Last Airbender fandom and was once the most popular ship. Some fans began to ship them as early as Book One: Water but the pairing became more popular at the end of Book Two: Earth and halfway through Book Three: Fire. Many fans collected evidence of this pairing and a popular series of YouTube videos titled "Zutara Evidence for the Intellectual Dummy" was released to try and make Zutara seem plausible. However, the popularity decreased when the series ended and Katara ended up with Aang instead.

Zutara has a lot of fanon. Also, an event called "Zutara Week" was started in 2008. Each day, there would be a theme and fans would draw fan art, write fan fiction, or even compile AMVs based on the prompt of the day. Zutara Week was such a hit that it stemmed many other weeks dedicated to ships, both within and outside of the Avatar fandom. Many fans were heartbroken when the Legend of Korra was announced and it was revealed that Aang and Katara had children. However, it was revealed that Zuko and Katara were both still alive after Aang passed away. Many fans began to hope that Zutara could happen in the Legend of Korra and began to wrote fan fiction about them getting together as elders.

Trivia

 * An Avatar Extra teased that Zuko was originally supposed to be Katara's love interest.
 * Katara's voice actress, Mae Whitman, voiced the love interest of Jake Long in American Dragon who coincidentally was voiced by Zuko's voice actor Dante Basco.