There are no psychological characteristics or psychopathology separating terrorists from the general population. Rather, it is group dynamics, with a particular emphasis on collective identity, that helps to explain terrorist psychology. Just as there is a diverse spectrum of kinds of terrorism, so too is there a spectrum of terrorist psychologies. Some terrorists, those in nationalist‐separatist groups, such as Fatah and the IRA, are continuing with the mission of their parents who are dissident to the regime. The opposite generational provenance is seen among social‐revolutionary terrorists, such as the Weather Underground and the Red Army Faction in Germany, who are rebelling against their parents’ generation, which is loyal to the regime. Four waves of terrorism can be distinguished: the “anarchist wave”; the “anti‐colonial wave” (nationalist‐separatist), with minority groups seeking to be liberated from their colonial masters or from the majority in their country; the “new left” wave (social‐revolutionary); and now the “religious” wave. With the communications revolution, a new phenomenon is emerging which may presage a fifth wave: lone wolf terrorists who through the Internet are radicalized and feel they belong to the virtual community of hatred. A typology of lone wolf terrorism is proposed. Copyright © 2014 John Wiley & Sons, Ltd.