Effectiveness of COVID-19 vaccines was first demonstrated in randomised trials, but many questions of vital importance to vaccination policies could only be addressed in subsequent observational studies. The pandemic led to a step change in the availability of population-level linked electronic health record data, analysed in privacy-protecting Trusted Research Environments, across the UK. I will discuss methodological approaches to estimating causal effects of COVID-19 vaccines, and their application in estimating vaccine effectiveness and quantifying waning vaccine effectiveness. I will present results from recent analyses using detailed linked data on up to 24 million people in the OpenSAFELY Trusted Research Environment, which was developed by the University of Oxford’s Bennett Institute for Applied Data Science.