There is, in the twenty-first century, an intense interest in the nature of wicked problems and the complex tasks of identifying their scope, viable responses, and appropriate mechanisms and pathways towards achieving improvement. This preoccupation is timeless, but the discussion over several decades has benefited from Rittel and Webber’s (Policy Sci 4(2):155–169, 1973) path breaking conceptualisation of wicked problems and the political argumentation needed to resolve them. This review revisits Rittel and Webber’s work and its enduring significance, reflecting upon its broad uptake and impact in the policy sciences, an impact that continues to grow over time. We revisit how the classic 1973 paper came to be published in Policy Sciences, its innovative depiction of social problems, its rejection of rationalistic design, its acknowledgement of the subjectivities involved in problem identification and resolutions, and the consequent need for argumentative-based solution processes. We find great resonance in the paper with contemporary problem solving preoccupations, not least that the political context is crucial, that argumentation must be transparent and robust, and that policy interventions may have consequences that cannot be easily controlled in open and highly pluralised social systems.