The relationship between Misa and Light begins when Misa finds out that the person who killed the killer of her parents was Kira. She was determined to find him, and at the end, with the help of her eyes, she found out his name and, with some researches in the net, she got his address and went to his house.
Since Misa is an idol, she was a very known person and Light's sister was happy to see her, but the boy was a bit upset. Once that Misa told him why she was there, in a first moment, Light didn't want her to stay with him, and then, he thought that the eyes of a Shinigami (that Misa has) could be helpful for him. So he told her to be his girlfriend, but since she was too famous, they couldn't see often each other. The main problem is that Misa is not patient and went to his school to meet him, and Light was in a mess with L. After this, the detective found out that Misa was involved in some ways with Kira, and decided to capture her.
During the period of captivity, Misa continues to believe in Kira and with Rem's help she exchanged her Death Note with Light's one. Anyway, at the end, she menages to get away from L's captivity, but she's always with Mogi. that pretends to be her manager in her activities with her job as idol.
Even after L's death, Misa and Light continue to work together as "accomplice", and Light manipulates her as he can, to gain the names of the people he wants to kill and letting her writing the names in her Death Note, so he can pretend to be a good substitute of L. His relationship with Kiyomi Takada will be very bad for them, because Misa is very jealous and they will have a meeting too, where the girl will get drunk.
At the end of the story, Light will be shooted by Matsuda and will die, calling Misa's name in order to write the names of the people that were trying to kill him. After a year, the 14th february, Misa commits suicide.
FROM MISA'S POINT OF VIEW ❤
Misa is really in love with Light, since she knew that he was Kira, the murderer of the killer of her parents. When she finds out that he's handsome and that he has a Death Note, as she has, she decides to devote her life to him. He tells her to be his girlfriend even if things will be difficult for them, but she accepts after he kisses her.
She's blinded from him, and does all things he told her to do, even if he says to kill people for him. Even if at the begin it was a bit a game, she will always get more in love with him. She's a passionate girl that only wants to give her boyfriend what she can, and she will do it everytime they see each other. We can see her jealousy with Takada Kiyomi when she finds out that Light had an affair with her, and will show her her childish personality in a dinner they made together.
Misa's passion has no limits, she will love and follow Light for the rest of her life, even when they kinda live together, but he beats her away although she dresses sexily. (Damn you Light T__T) At the end, Kira's secret will be revealed and, one year after his death, she will commit suicide. I think it is for love, we don't know exactly why she did it, but her love was too big, since she decided to make the exchance of the Shinigami's eyes two times.
I would describe Misa's love for Light as pure and passionate.
FROM LIGHT'S POINT OF VIEW ❤
As all people who read Death Note know, Light is not the person who's looking for love. His lust for power is bigger, his only desire is to make his justice. He has a difficult relationship with Misa, because when they meet each other, he didn't agree with her to become his boyfriend, but changed idea when she told him that she had the eyes of the Shinigami and could see the names of people in their forehead.
So, they became lovers, even if Light's love was just for her eyes. He always tried to be kind with her, even if when he was nervous, he treated her very badly. In few words, he had what he wanted. He just played a bit with her, but he was never interested in love in general. I think that, in any case, he had a cute relationship with Misa, instead of all the other charaters.
I describe his love for Misa as cold and unappealing.