The twentieth century has rightly been dubbed the Century of Genocide. Will the twenty-first see a continuation of events that intensified in the 1990s -- events which witnessed genocide breaking out in Bosnia and Rwanda, being averted in Kosovo, and continuing in Sudan? Or will the human rights norms that evolved in stages after the Second World War and, by the very end of the twentieth century, began to intrude into the conduct of foreign relations, develop a momentum and eventually usher in a lasting period of universal harmony? As an historian of genocide rather than a predictor of it, my responses to these questions can be nothing other than tentative, even trepidatious. And yet in looking at what the nature of genocide might be in the twenty-first century, my analysis will be based on an appreciation of where genocidal outbreaks have come from over the course of the past century, and how (and under what circumstances) they have been resolved. From this it might be possible to consider whether or not genocide is to be a social problem for the twenty-first century; whether its worst expressions have been left behind in the twentieth; and whether or not genocide is, or will become, a defining characteristic in the future. There can be no clear-cut answer to these questions, owing to the many variables existing on a global scale, but some broad suggestions can be offered as to where developments might lead.