Understanding why people become involved in terrorism is vital to inhibiting recruitment and radicalisation, and therefore preventing terrorist attacks. The question of why people support, engage with, and participate in terrorism is addressed in this thesis. Insights into the causes of terrorism and the process of radicalisation are garnered from social and evolutionary psychology in an effort to add an additional interdisciplinary layer of theoretical understanding to existing political science research. The central argument made in this thesis is that certain psychological processes (social identity), and mechanisms (parochial altruism), influence people to favour ingroups and disfavour outgroups in light of particular intergroup cues. Although social identity theories and the concept of parochial altruism pertain to the same argument for bias towards ingroups, which may also entail bias against outgroups, they arrive at this position in different ways and therefore offer alternative insights into what conditions trigger this bias, and responses to it. A novel experimental paradigm with student participants generated data to investigate the evolved mechanism parochial altruism. Social identity theories were applied to certain features of the radicalisation process to explain how and why identification with the Muslim Umma (worldwide community) occurs, which is a central feature of radicalisation in Al-Qaeda type groups. The insights challenge some of the assumptions made by scholars about the nature of radicalisation and terrorism. This thesis considers the process of radicalisation to be rooted in, and influenced by, normal psychological processes and mechanisms that are present in all humans. Although there are caveats, this thesis provides new avenues of exploration and further research to investigate terrorism, radicalisation, and intergroup conflict more generally.