This chapter provides a brief overview of some of the core psychological approaches. The psychology of terrorism as a field has transformed over the years from homing in on psychological abnormality to the rejection of such ideas and the development of models of radicalisation. Despite some theoretical progress and a more rigorous scientific approach to studying the psychology of terrorists, as well as an explosion of publications, the field continues to be hampered by a lack of primary source data and access. Counterterrorism policy in the UK includes 'terrorism offences' that do not even involve actually committing terrorist violence, further muddying the conceptual waters. Terrorist grievances are those political, social, economic, and cultural issues and goals that are all but dismissed by scholars and policymakers looking to psychological abnormality to explain terrorism. Engagement and involvement in terrorism is not a static state, but a gradual process, which tends to involve transitioning through different stages.