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Understanding social-ecological systems (SES) is crucial to supporting the sustainable management of resources. Agent-based modelling is a valuable tool to achieve this because it can represent the behaviour and interactions of organisms, human actors and institutions. Agent-based models (ABMs) have therefore already been widely used to study SES. However, ABMs of SES are by their very nature complex. They are therefore difficult to parameterize and analyse, which can limit their usefulness. It is time to critically reflect upon the current state-of-the-art to evaluate to what degree the potential of agent-based modelling for gaining general insights and supporting specific decision-making has already been utilized. We reviewed achievements and challenges by building upon developments in good modelling practice in the field of ecological modelling with its longer history. As a reference, we used the TRACE framework, which encompasses elements of model development, testing and analysis. We firstly reviewed achievements and challenges with regard to the elements of the TRACE framework addressed in reviews and method papers of social-ecological ABMs. Secondly, in a mini-review, we evaluated whether and to what degree the elements of the TRACE framework were addressed in publications on specific ABMs. We identified substantial gaps with regard to (1) communicating whether the models represented real systems well enough for their intended purpose and (2) analysing the models in a systematic and transparent way so that model output is not only observed but also understood. To fill these gaps, a joint effort of the modelling community is needed to foster the advancement and use of strategies such as participatory approaches, standard protocols for communication, sharing of source code, and tools and strategies for model design and analysis. Throughout our analyses, we provide specific recommendations and references for improving the state-of-the-art. We thereby hope to contribute to the establishment of a new advanced culture of agent-based modelling of SES that will allow us to better develop general theory and practical solutions.