It was widely known and accepted for a long time that van der Sloot killed her. They just didn't have the evidence to try him for it. He stayed in the news because of the other killing and because he tried to extort $250,000 from Natalie's parents in exchange for the location of her body. They still wouldn't know with 100% surety that he did it, had he not confessed (which he did as part of a plea deal in the extortion case) and passed a polygraph about it.
According to him she refused his sexual advances and kneed him, and he got pissed and killed her by kicking her in the face and slamming a cinderblock into her skull. Then he threw her body into the ocean. May he never see the light of day as a free man.