Present day criminality in Western Europe can be broken down into two main classes. First, the increasingly technical, clever, subtle and modern forms, which are organized and perhaps foreshadow large scale 'European' criminality (e.g., white collar crime, politically motivated crime). The second significant crime form is traditional crime usually caused by poverty. The increase of the latter is associated with cultural and social disorganizaton and with anomy, especially among among migrants. Recent criminal policy tends to increase penalties for such crimes as kidnapping, highjacking, drug offenses, and on the other hand, decriminalize such offenses as vagrancy, adultery, pornography. However, more attention should be given to transfrontier, transnational and international forms of criminality. The United Nations should stimulate research on these crimes and ways to fight them, since traditional approaches are not sufficient. Footnotes are included.