The relationship between the original hybrid, Niklaus Mikaelson and the tribrid doppelgänger, Alexandria Gilbert is a complicated, but a popular and powerful romantic pairing, and a significant relationship in the series first began on antagonistic terms. They first interacted in Season 2 episode The Last Dance, when he was in Alaric's body to spy on both doppelgängers. He was told by one of his witches that he and the latest doppelgänger would be together. At the end of Season 2, Alex leaves with Klaus and Stefan. In Season 3, Klaus tries to get closer and closer with Alex; trying to fulfill the prophecy that was given to him by one of his former witches. They share a kiss, sparking the start of the prophecy. In The Sun Also Rises, he sacrifices her sister and then fed his blood to her, so that she'd be immortal making her the first Tribrid to walk the earth.
In Bring It On, when Alex was still infected with dark magic they had slept together so that she could put up the act that she was back to normal. It was later revealed when they met again in New Orleans that Alex was pregnant with his child, their daughter Hope Mikaelson, who they conceived during The Vampire Diaries. Their main priority is to protect Hope. However they have disagreements over the best way to protect their daughter.
Unfortunately, their relationship takes a turn for the worse when Alex tried to take Hope away from Klaus. Klaus became hurt/enraged by this attempt and he had Dahlia place the Crescent Curse on Alex and her pack, as punishment for trying to take their daughter away from him. They are no longer friends or allies after this; they have become enemies once again.
In You Hung the Moon, after six months, Alex and her pack are temporarily released from the curse, and she confronts Klaus for what he did to her and fights him, eventually resulting in her taking custody of Hope from him. They continue to share an antagonistic rivalry, but are allies for the sake of their daughter. However, they somewhat reconcile later on and end up running away together with their daughter and Alex's brother after Klaus' sireline is broken, which sends all of his enemies rushing to kill him.
In Haunter of Ruins, they've rekindled their relationship. Klaus talked with Hope, Jax, Nina, and Lily if it was okay that he asked Alex to be his wife. The triplets knew that their mother loved him and give him promotion but only if he loved her for the rest of his life to which he said he would. Later that night Klaus proposed to Alex to which she accepted.
They are referred to as "Klalex" by fans.