Genghis Khan actually died fairly early, only twenty years after the Mongols emerged from the steppe and started their conquest. His sons and their sons are the ones that finished conquering and uniting China, expanding to the west, to the middle East and into Russia and Eastern Europe. Most of Mongol history happened after Genghis died, so this question is kind of impossible to answer. Most of the interesting things the Mongols did happened under his successors.