EruRi

Eru(vin)+Ri(vaille) is a ship between Captain Levi Ackerman and Commander Erwin of the Attack on Titan series.

Canon
Erwin and Levi places deep trust and respect for each other to a certain extent. Levi places full trust in, obeying his every command and judgment.

However, this did not stop Levi from speaking in his usual rude manner around him. Erwin was also one of the few people that could maintain casual conversation with Levi, which able him to exchange brief banter with one another on equal grounds.

In Chapter of 72,when the meeting ends, Levi closes the door behind the other members to talk to Erwin privately. Levi made it clear that he is concern about Erwin’s health and tell him to stay put. Erwin stubbornly says no. Levi made statements if he dies the mission is over. As a last effort Levi threaten Erwin that he will break his legs. Erwin made it clear to him that he still want to be on the frontlines fighting. What Erwin said clearly upsets Levi but he realize that he can’t change his mind because Erwin is stubborn and will do anything to archive his dream.

Seeing the inevitable defeat of the Survey Corps, Erwin begins to grieve over the failure of his attempts to learn the truth of the world. He thinks back on the many soldiers that died for the sake of humanity which he use as an advantage to archive his dream. Erwin began to question his dream as a childish delusion. Levi tries to encourage him and said it’s the survey cops wouldn’t be able to come this far without him. Levi then told him to give up on his dreams and die and to lead the new recruits into the battle. Despite his dreams coming to a bitter end Erwin is relieved.

In chapter 83-84 Levi changes his mind on saving Armin when a soldier delivers a critically wounded Erwin to him. He settles on saving Erwin, which angers Eren. Levi thought back on the dreams that Erwin had but before he could inject the needle Erwin knock the needle out of his hand. Erwin smash the case into Levi’s chest and thanked him. This led to Levi chossing to let Erwin die peacefully. Hinting that he care enough for Erwin to let him die knowing that Erwin probably wouldn’t want to become a titan knowing what he had done as a commander. Finally, Levi tells Erwin his promise about defeating the breast titan will have to wait as he dies.

Fanon
Many fans have notice in Attack on titan and in Attack on Titan: Regrets that the relationship between Erwin and Levi is unique, based on deep trust and respect. Also they have a longer history together so they have a strong personal bond. It’s clearly obvious that they worried for each other well being and the well being of their comrades as well. Which goes to show that they are more than just ‘co-workers.’ Levi always did followed Erwin’s footsteps especially in the anime you’ll notice that Levi constantly follow him around in certain scene (like in episode 22, season one). It’s unknown what Levi felt but after Erwin’s death he did claim that he let his personal feelings which led to his decision. Also it appears he was upset over his death.

According to Isayama's interview he was asked about Levi's preferred type of person and answered "A type of woman he likes? Since he’s short, small people tends to like tall people… I guess he might like tall people.” Since Erwin is one of the tallest in the series other than Bertolt Hoover it won't be surprise that he possibly took a liking toward Erwin. Like other ships this can lead to conflicts with other ships the fan have Levi and Erwin like Eremika,Levihan, Rivetra,Erumike, EruRi (especially), and other ships.

Many shippers had created comics and arts to show their support of the ship. References:

http://attackontitan.wikia.com/wiki/Falling_Axe

http://attackontitan.wikia.com/wiki/Midnight_Sun

http://attackontitan.wikia.com/wiki/Night_of_the_Battle_to_Retake_the_Wall

http://attackontitan.wikia.com/wiki/Choices_and_Consequences