I hear Elijah has refused you the cure, and in return you have refused my freedom. Shame on you both. But while you boys sort our your problems, I have one last thing to offer you. I have caught wind that there is a witch in New Orleans named Jane-Anne Deveraux plotting a move against you. Hunt her down. What she has to say will rattle you so deeply to your core that chasing little old me will be the least of your concerns. It's been a fun five centuries Klaus, but I've worn down too many good heels running from you.
Love, and hate.
The relationship between Klaus and Katherine Pierce has been antagonistic. In the beginning Klaus was kind to her, but later, when Katherine discovered that he needed her for the sacrifice, she ran away. She killed herself with Rose's blood in her system, and when she awoke, she fed on Rose's house mate in order to become a vampire. Once she turned, her blood became useless to Klaus, as he needed the blood of a human doppelgänger. Klaus' revenge was to kill Katherine's whole family.
They met in 1490, after Katerina (Katherine) was disowned by her family for having a child out of wedlock, and exiled from her home in Bulgaria. She immigrated to England, where she eventually met Elijah and Klaus, who at the time were noblemen. She became friends with them for a short time, but as soon as she found out their intentions with her, she ran away, and took the moonstone with her. She then became a vampire after she tricked Rose into feeding her her blood. Later, Klaus found her the village in Bulgaria where she was born, and slaughtered her whole family in punishment for thwarting his plans.
In The Last Dance, Klaus who still was in Alaric's body, gets information on Elena and her friends. He then compels Katherine to hurt herself by sticking a knife in her leg and repeating it again and again. Later on, he asks her for her opinion on what shirt to wear to the dance, he gets surprised by the many weapons found in Alaric's Apartment and asks her who Alaric is.
In The Last Day, Damon asks Katherine where Klaus has kept Caroline and Tyler. She replies by giving him the address. Klaus returns to Alaric's Apartment and is immediately suspicious of Katherine. He compels her to tell him what she has been doing but, as she is taking vervain, she is able to lie. He is still suspicious and 'compels' her to take off her bracelet, walk to the window and stand in the sunlight. Katherine has to do it and screams. Eventually Klaus believes she is compelled and says she needs to do something for him. Klaus later compels Katherine to phone Jenna so he could get his vampire for the sacrifice.
After Stefan gives in to Klaus plan, the hybrid tells Kat to bring Damon the cure, because he will die soon of a werewolf bite. Katherine runs away fastly, because she drank vervain and so, can't be compelled anymore, not even by the powerful Klaus. Despite this fact, Katherine gives Damon the cure and runs away from Mystic Falls to hide from Klaus.
In 3x04 Katherine shows up near Klaus and Stefan. She talks with the Salvatore about teming up with him to find a way to kill Klaus, but Stefan refuses.
So Katherine decides to create a new plan and makes a road trip with Damon to free a very old vampire named Michael, who claims that he can kill Klaus.
They will later learn that Mikael is Klaus' step father.
In 3x09 Katherine pretends that she's Elena and meets Klaus at a party at Tyler's house. They talk and it's obvious that Katherine is pretty nervous. Klaus flirty beginning, turns into a warning that they can try to kill them, but eventually it won't work.
In the end, the plan fails like Klaus predicted. Katherien encurages the now freed Stefan to start his own revenge on Klaus.After that Katherine disappears again.
The race to get the cure to end the status of vampirism ends, as Katherine surprisingly shows up and takes it.
Soon after Klaus finds that out and wants to find her even more than ever. He thinks that she will force him to take the cure, so that he's vulnerable and can be finally killed. In reality, Katherine wants to negociate with Klaus to regain her freedom: She will give him for her liberty the cure, so that he can do with it whatever he wants.
For this negoociation she needs Elijah, who turns away from her and refuses to give the cure to Klaus. Consequently Klaus refuses Katherine her freedom, who afterwards sends Klaus a special letter:
"...while you boys sort out your problems, I have one last thing to offer you. I've caught wind, that there's a witch in New Orleans called Jane-Anne Deveraux plotting a move against you. Hunt her down. What she has to say will rattle you so deeply to your core that chasing little old me will be the least of your concerns. It's been fun five centuries Klaus, but I've worn down too much good heels running from you.
Love and hate,
Only thanks to Katherine, Klaus can hinder the witches' plan.
As Klaus is in New Orleans, Katherine has a talk with Rebekah, in which she admits, that Klaus and she are the same: "We manipulate, we thirst for power, we control, we punish, but our actions are driven by one singular place deep inside: We're alone... and we hate it."
In 4x22 and 4x23, Katherine wants to achieve Silas' immortality, so that nobody can ever scare her anymore. But it went the complete different way and Katherine becomes human.
So the question is: If Klaus finds out that his former doppelganger is mortal again, will he use her as his new blood source to create a new army of hybrids?