This article provides a critical review of key theoretical positions relevant to border control and sets out an agenda for developing these ideas. In 2005 Mythen and Walklate published a theoretical milestone for the study of terrorism in their article ‘Criminology and terrorism: Which thesis? Risk society or governmentality?’. Those authors reviewed two theories of risk, considering how each might contribute to understanding ‘new terrorism’. Inspired by ‘Which thesis?’ we review, contrast and compare three key theoretical contributions relevant to penology, criminology and border control: Stump’s ‘crimmigration’ thesis, Bosworth and Guild’s adaptation of the ‘new penology’ perspective, and Krasmann’s critique of Jakobs’ ‘enemy penology’ thesis. The article consolidates these important theoretical strands into one critical discussion, highlighting the growing relevance of the pre-crime literature to the study of borders, and signposting potential theoretical developments within border criminology that build on these foundations.