ZoLu

"Luffy? Can you hear me? Sorry for worrying you. If I don't become the world's greatest swordsman, that would be a problem for you, wouldn't it? I...I will...I WILL NEVER LOSE AGAIN! Until I defeat him and become the greatest swordsman, I'll never be defeated again! Any problems with that, Pirate King?!"

- Zoro. "Why should I be scared of Kaido? If my captain gives the order, I'll just follow."

- Zoro in episode 1014

"Who, Zoro?! Don't worry about him! He can pull through anything!"

- Luffy.

ZoLu is the slash ship between Roronoa Zoro and Monkey D. Luffy from the One Piece fandom.

Romance Dawn Arc
Luffy meets Zoro while he's being held captive by some marines who agreed to set him free only if he survives with no food or water tied up under the sun for a month. Luffy admits to him that he's looking for a crew so he can become King of the Pirates, to which Zoro replies that there's no way that he'd join his crew since he's 'weaker'. Luffy then says that he wouldn't want Zoro on his crew since he's got bad reputation. When Zoro asks Luffy to feed him the rice that a kid prepared him which has been thrown on the ground and was filled with dirt, Luffy deducts that he's a good guy. When Luffy found out Zoro's going to be executed in 3 days and that Helmeppo lied, he proceeds to beat him up and declares that he's gonna make Zoro join his crew. As Luffy and Coby head back to the marine quarters, Zoro finds out what Luffy's done when he found out about his execution. Once Luffy gets his swords back and protects Zoro from gunshots, Zoro comes to admire Luffy's strength and tells him that he's earned a crewmate.

Orange Town Arc
After Luffy's been tricked into being captured by the Buggy Pirates due to Nami, Zoro finally arrives to the island and looks for Luffy. When he arrives to set Luffy free, Buggy engages a fight with him and wounds him. Luffy tells Zoro to leave at which Zoro refuses, but then catches on Luffy's plan just through eye contact. After firing at the Buggy Pirates, Zoro carries the cage Luffy's in and leaves.

When Zoro arrives to town, he goes to sleep and is put in care in a shelter by the mayor. After Luffy's cage is destroyed by an enemy, he tries to ignore the fight to go look for Zoro which failed and he ends up engaging in the fight. Buggy then fires a cannon ball at the shelter Zoro's staying in, which worries Luffy, but turns out he came out alive. After Luffy attacks the Buggy Pirates recklessly, Zoro admits that he 'worried him for nothing'. When Buggy tries to intervene in Zoro's fight, Luffy stops him and says "Keep your mitts out of Zoro's duel!" After Zoro's victory, he admits to being a pirate and tells Luffy he's gonna rest. Luffy tells him not to worry and that he's gonna take it off from there.

Baratie Arc
Nami, Usopp and Zoro are all sat on a table when they call Luffy, who's been hired as a 'chore boy' because of the damage he caused. Zoro then teases Luffy about how he won't get to enjoy the food here which annoyed Luffy and made him drop a booger in his drink. Zoro pretends he's about to drink it then immediately makes Luffy drink the cup.

Near the end, Zoro channels a fight with Mihawk, which in he immediately loses to. Luffy thinks Zoro has died, which angers him to the point where he tries to attack Mihawk. Mihawk dodges and tells him that Zoro's alive, which Luffy is glad to hear. After being defeated, Zoro's ashamed and declared that he'll never lose again so he'll become the world's greatest swordsman and not disappoint him, even calling him King of the Pirates. Although Mihawk hasn't seen them really interact, he tells Luffy that they both make a great team and that he hopes to meet them again.

Arlong Park Arc
After Zoro beats the fishmen up, he wonders where Luffy is, saying that he promised he'd bring Nami back to him. When Nojiko's about to bring up Nami's past and Luffy says he's uninterested and leaves, Zoro said not to worry about him and that's just how he is.

Loguetown Arc
Zoro and Luffy both go to a restaurant together. After eating for a while, Zoro realises they both don't have any money to pay up. But that's soon resolved after they both unintentionally take money from Buggy, who's been following them.

Whisky Peak Arc
After finding out the village's true intentions, Zoro gets in a mess with the Frontier Agents and the other people residencing on said island. When Luffy wakes up and is still under the impression that the villagers were innocent, he starts a fight with Zoro who tries repeatedly to explain the situation which failed. Zoro thought that it might be a good test to see who's the strongest between the two, until Nami intervenes and stops them both. Luffy soon realises that it was a misunderstanding.

Water Arc
Zoro expresses that the crew must hold respect for Luffy, even if he's "a complete idiot". He says the crew is better off with someone who doesn't respect their Captain. Zoro also says that if his Captain is someone who will let people trample all over him, he might as well leave the crew. Luffy, Nami and Chopper are left shocked by what he said, but after some thought Luffy says that he agrees.

Enies Lobby
Luffy orders Zoro to cut some enemies up because they're standing in the way, which Zoro replies to with 'Sure.' without even thinking it over, which surprised the others.

Thriller Bark Arc
Throughout the story, Zoro has expressed that if Luffy would ever come in the way of his dreams, he would leave the crew or even kill him. But during this arc, Zoro seemed to have changed his mind about him, saying that he can't complete his dreams and ambitions without protecting Luffy's. After he almost dies by taking all the damage Luffy's endured so Kuma spares him, he says that nothing happened. He does so because protecting Luffy is what he's supposed to do as part of his crew, he doesn't need that recognition because all the strawhats already know that they'd stake their lives for anyone on the crew. He also expresses how he doesn't want Luffy knowing he caused one of his friends pain.

Sabaody Archipelago Arc
During the big fight, Zoro gets hit by Kuma, which devastates Luffy enough for him to repeat his name and shouting it at least 6 times. He also begins to remember flashbacks of them together. After all his crew is gone, Luffy beats himself over not being strong enough to protect any of them.

Impel Down Arc
Before revealing his true identity, Bon Clay was disguised as Zoro. Luffy seems happy to see him, screaming his name in a surprised yet excited tone. When Bon Clay takes on his real form, Luffy exclaims “I'm so disappointed that you're not Zoro, but at least you're alive!"

Post War Arc
After Mihawk comes back from Marineford, he finds Zoro outside his castle. Zoro finds out that Luffy was there during the war and asks if he was okay, Mihawk tells him that he was probably still alive, but that his heart has dealt great injury. When Zoro finds out that Ace died right in Luffy's arms, he was the only strawhat who seemed like he was on the verge of tears. After beating the baboons outside of the castle, Zoro bows down to Mihawk begging him to train him. Mihawk says that he's only embarrassing himself and proceeds to ask why, which Zoro replies to saying "I want to beat you." Mihawk ends up accepting, but deduced that there was another reason as to why hes asking Mihawk for guidance, saying "Seems like you found something more important than your ambition" and thinking "When a man like you swallows his pride, it's always for someone else."

Fanon
On AO3, ZoLu is the 2nd most popular ship for both Zoro and Luffy, as well as the 4th most popular ship in the fandom.

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Trivia

 * Zoro and Luffy's specific colors (green and red) are complementary colors.
 * Luffy and Zoro's specific numbers are 01 and 02. Luffy's number is also 56 (Rubber; "Go" = 5, "Mu" = 6), and in chapter 872 color spread Zoro is shown to have this number on his chest.
 * Luffy's favourite food is all kinds of meat, while Zoro specifically likes sea beast meat. This means that Zoro shares his like of one kind of meat with Luffy.
 * Zoro's least favourite food is chocolate, because it's too sweet, while Luffy does like to eat them (as he did love the sweets in the Fish-Man Island). In chapter 800 Luffy states that he doesn't really like alcohol that much, while alcohol is to Zoro what meat is to Luffy. This means that they both can share food or drinks that they are not that fond of with each other so nothing gets really wasted.
 * If Zoro and Luffy wouldn't be pirates, their jobs would be a police officer (Zoro) and a firefighter (Luffy).
 * Zoro and Luffy (with Brook) are the only members in the Straw Hat Pirates who bathe only once per week.
 * Luffy and Zoro's personalities and thought processes (ideas) are very similar, though Zoro can be more strict and Luffy can be more outgoing.
 * Luffy and Zoro also have scars in similar places on their bodies: One scar on the left side of their faces (under Luffy's eye, and over Zoro's eye) and a bigger scar on their chest.
 * Both Zoro and Luffy are the only ones in the Straw Hat Pirates who can use all three types of hakis:
 * Kenbunshoku Haki (aka Observation Haki)
 * Busoshoku Haki (aka Armament Haki)
 * Haoshoku Haki (aka Conqueror's Haki, Color of the Supreme King), which is a type of haki that the individual has to be born with to be able to use it, and is also known as very rare ability that only one in several million people are born with.
 * Zoro's animal resemblance is shark, and in the cover of chapter 3 (in which he was introduced) shows a picture of Luffy riding on the back of a shark.
 * However, Zoro is later represented also as a tiger in chapter 651 color spread, and in Color Walk 9 Tiger cover we see only Zoro and Luffy (and Chopper) with a giant tiger. In chapter 394 color spread we see Luffy standing on a tiger (with Chopper), and Luffy also rides a tiger hoverbike in chapter 872 color spread.
 * Luffy's animal resemblance is monkey, and in chapter 174 cover page Zoro is sharing a bath and drinking sake in a hot-spring with a pack of macaques (also known as the "snow monkeys").
 * In chapter 589, that is part of Luffy's childhood story with Ace and Sabo, Zoro is very briefly seen training in his own village while Dragon's (Luffy's father) ship sails past him in the background.
 * Zoro is often seen to fight the second strongest enemy in the One Piece series, while Luffy usually takes on the main big bad guy. Though sometimes Zoro will first fight or even win (briefly) against the main bad guy (e.g. Fish-Man Island Arc).