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Climate change is a product of the Anthropocene, and the human-nature system in which we live. Effective climate change adaptation requires that we acknowledge this complexity. Theoretical literature on sustainability transitions has highlighted this and called for deeper acknowledgment of systems complexity in our research practices. Are we heeding these calls for systems' research? We used hydrohazards (floods and droughts) as an example research area to explore this question. We first distilled existing challenges for complex human-nature systems into six central concepts: Uncertainty, multiple spatial scales, multiple time scales, multimethod approaches, human-nature dimensions, and interactions. We then performed a systematic assessment of 737 articles to examine patterns in what methods are used and how these cover the complexity concepts. In general, results showed that many papers do not reference any of the complexity concepts, and no existing approach addresses all six. We used the detailed results to guide advancement from theoretical calls for action to specific next steps. Future research priorities include the development of methods for consideration of multiple hazards; for the study of interactions, particularly in linking the short- to medium-term time scales; to reduce data-intensivity; and to better integrate bottom-up and top-down approaches in a way that connects local context with higher-level decision-making. Overall this paper serves to build a shared conceptualisation of human-nature system complexity, map current practice, and navigate a complexity-smart trajectory for future research.