Caroline and Tyler

This is the relationship between the vampire, Caroline Forbes and the former hybrid/currently triggered werewolf, Tyler Lockwood.
Originally, the two did not like each other. She thought he was hot-headed and temperamental, and he thought that she was spoiled and selfish. After Caroline breaks up a fight between Tyler and Matt, and Tyler kills Sarah, she's the first to realize that he has activated his curse. Tyler, suspicious of her, soon discovers that she's a vampire, only after accusing her of also being a werewolf due to her strength. She tells him that she's the only vampire in Mystic Falls, only in an effort to protect Stefan and Damon. She comforts him throughout his transition.
After discovering that Caroline could have died by being so close to him, Tyler kisses her. Shocked, she slams the door in his face and later explains about her existing feelings for Matt. When Jules arrives, she informs Tyler that Caroline lied about being the only vampire and that she knows what happened to his uncle, Mason. Tyler confronts Caroline, believing she betrayed him. After Tyler hesitates in saving her from Jules, Caroline turns her back on him, and he leaves town with Jules without saying goodbye.
Greta and Maddox kidnap both Tyler and Caroline upon his return to town. Caroline informs Tyler that they have been lined up to be executed in Klaus's sacrifice, however, Damon arrives to save Caroline. She convinces him to save Tyler too, and ends up running from Tyler with Matt after he turns into a werewolf. Later, Caroline informs Tyler that Matt broke up with her and he comforts her.
Tyler and Caroline form a strong friendship. Caroline's jealous when Tyler brings Sofie to Elena's party. She compels Sofie to leave, leading to Tyler to confront her. They end up kissing and then sleeping together. However, when Caroline tries to sneak out, Carol kidnaps her and delivers her to her father, Bill to be tortured. Tyler and Liz save her and she soon begins a relationship with Tyler. However, upon Klaus's return, he turns Tyler into his first successful hybrid. As a result, Tyler becomes sired to Klaus and begins to rely on Rebekah for blood. Tyler leaves town to break the sire bond and, when he returns having been successful, is unhappy to learn that Klaus has fallen in love with Caroline. After Klaus's "death," Caroline tearfully kisses Tyler goodbye, unaware that Klaus has in fact, taken over Tyler's body.
Tyler later returned to his own body. When Klaus bites Caroline, Tyler carries Caroline's body to where Klaus is, saying that he deserves to watch her die. After Klaus heals Caroline, he threatens to kill Tyler but she convinces him not to. Instead, he gives Tyler a "head start" and tells him to start running. Thus, Caroline and Tyler bid a tearful farewell, promising it wouldn't be forever. Before Klaus leaves town, he tells Caroline he has a graduation present for her and gives Tyler the freedom to return.
Tyler defers from college much to Caroline's sadness. He returns to comfort her about Bonnie's death. They have a brief reunion, but Tyler reveals that he plans to kill Klaus, thus leaving town again. She warns him that it will be over between them if he leaves, but he does so anyway. When Tyler returns to Mystic Falls, he initially wants to get back with Caroline however their relationship takes a negative turn after he finds out that she slept with Klaus. He angrily confronts Caroline about it, ending their romantic relationship. When the other side collapses and Tyler comes back, him and Caroline share a brief hug.
They are referred to as "Forwood" or "Tyroline" but less commonly, "Cyler" or "Tyline" by fans.