The Treaty on the Prohibition of Nuclear Weapons (TPNW) is a landmark agreement in the history of the nuclear disarmament movement. It was negotiated against the wishes of the nucleararmed states and many of their supporters and this context defines the challenges and opportunities for its universalisation. We argue that universalisation should be understood as a strategy for maximising the authority of the treaty and its core norms and principles across four categories of state: disarmament advocacy states, a nonnuclear-armed state majority, nuclear client states, and nucleararmed states. We show how these norms and principles are extensions of what already exists, particularly for non-nuclear armed states, but that making these connections will require targeted and sustained political work. We argue that states parties to the TPNW working with civil society will need to engage non-nuclear armed states with a range of normative arguments for the treaty and against the narratives of its critics. This can be done through a range of outreach activities based on other treaty universalisation campaigns, and we set these out in detail. Engaging nuclear client states and nuclear-armed states will be more difficult and require a different approach based on carving open a discursive space in which the TPNW's humanitarian, ethics, and risk rationales must be confronted. Political opposition will be formidable, but the purpose of the TPNW is to influence the nuclear weapons policies of nuclear-armed states, and increasing the authority of the treaty's norms and principles through universalisation strategies will be essential to this.