The view of the Middle Ages is summed up in this T-and-O map :
... with Asia populated by Semites, Africa by Hamites and Europe by Japhethites. The traditional genealogies are covered in the Wikipedia article.
We might wonder, however about some aspects of this. Can Arabs and Japanese really both be sons of Shem, for example? Given our more extensive knowledge of the Oriental peoples (and their extension into the Americas), might we have cause to recategorise?
In one alternative scenario, British Israel/ Christian Identity types regard white men as Semites and Orientals as Japhethites. A theory which has been tickling my nous of late, however, is that of Arthur Custance, in which the traditional understanding of Japhethic as white or Indo-European is retained, Semitic is used in its restricted sense to refer to various Middle Eastern peoples, and Hamitic to all of the remainder of humanity: