Totalitarian regimes and terrorist groups striving to create them are characterized by ideologies with lexicographic preference orderings. This means that they demand that their followers sacrifice everything, if required, including the lives of others and of themselves to reach the aims postulated. More than twenty such regimes have existed, from the Mongolian and Aztec Empires among the first, to much later Nazi Germany and the Communist Soviet Union, and in recent years to the rule of the Taliban in Afghanistan and ISIS in Syria and Iraq. This means that the respective ideologies are usually very different, but that all follow a lexicographic preference order. This chapter studies the development, success, and demise of such regimes, which usually persecute, torture, and even kill nonbelievers, and often are engaged in bloody wars of expansion with many victims. This is also the case concerning their secularly or religiously based aims, which, moreover, characteristically control their behavior concerning the lifestyle of their populations, the arts, and their culture. Totalitarian regimes that have reached their aims are called mature ideocracies. They are characterized by the fact that the whole population has accepted (or at least pretends to accept) the ruling ideology.