This literature review explores the concept of emergence in public governance, and the need for building anticipative capacity in public organisations. The purpose of this review is to explore how public organisations can deal with issues that emerge in their environment. Emerging issues are characterised by a great deal of complexity and uncertainty, and therefore create challenges for static public governance arrangements. Dealing with emerging issues requires that organisations and systems build anticipative capacities. The literature review summarises recent but also less recent organisation theory focusing on organisational improvisation and on complex governance arrangements. This literature presents an alternative way of both analysing organisations and of organising beyond static and highly proceduralised or systemised conceptions. New organisational arrangements to cope with emergence sometimes appear counterintuitive, and they sometimes appear to defy the rules of economy, efficiency, democracy and the rule of law. As is evident from Bourgon’s ‘New Synthesis’ framework, an organisation or system that facilitates emergence needs to make a trade-off with other objectives. While such arrangements are good at anticipating change and at detecting trends, they come with challenges to the performance, compliance, and the resilience of the public sector.