Who settled Japan and made it what it is today?

I know that historians are aware that people lived in Japan from the stone age as farmers and fishermen. But who came and turned into what we think of as Japan, with samurai, the kanji, and the ancient Japanese culture? I have read that there is a disagreement between historians, that some believe it to be the Koreans, others believe it to be from the Han Chinese. Which was it? And who were the people who lived there in the BC times?