The COVID-19 response continues to be driven by epidemiological priorities, and yet, the epidemic and responses are situated within specific political and health system contexts. Social science brings an understanding of context and draws attention to politics, power and social difference. There are four critical social science priorities for COVID-19 research and policy in the long term. First, political-economic insights can support the design of public health measures and elucidate how public health responses are produced by political systems. Second, a better understanding of the political and social structures that relate to vaccine confidence will improve public trust, acceptability, effectiveness and uptake of COVID-19 vaccines and therapeutics. Third, development of social science perspectives on health and governance is vital to inform and untangle the complicated ways in which nationalism interacts with public health measures. Finally, social science inquiry can reveal how individuals and communities perceive, understand and construct COVID-19 risk and severity and seek help. These insights support building trust and good relations between local and international research and programme teams and between communities and researchers that will enhance confidence in the development, research and deployment of vaccines and other COVID-19 control measures.