© 2022 Informa UK Limited, trading as Taylor & Francis Group.The seismic assessment of concrete gravity dams is a problem of prediction of cracking and the corresponding consequences. With the widespread use of general-purpose finite element programs, the work in the field has shifted towards quantifying the behaviour in a framework for assessment. The nonlinear analysis and coupling with foundation–reservoir interaction, conversely, is still a challenging task. The modelling approach has significant effects on the analysis results and the assessment framework. The field remains an active area for research with many outstanding issues regarding damage quantification and assessment compared to any other major infrastructure component. A comprehensive overview of the seismic assessment of gravity dams is presented in this work with the goal to outline the issues in the field. Different models and modelling choices are compared in the context of damaged state assessment of gravity dams. The links between practical difficulties and theoretical issues are critically discussed. The aleatoric and epistemic uncertainties in the field, and their sources, are presented. Areas of future work are identified for improvement in seismic assessment as well as reducing and quantifying the uncertainties in the prediction of damaged states for concrete gravity dams.