Abstract. The unprecedented use of Earth's resources by humans, in combination with the increasing natural variability in natural processes over the past century, is affecting evolution of the Earth system. To better understand natural processes and their potential future trajectories requires improved integration with and quantification of human processes. Similarly, to mitigate risk and facilitate socio-economic development requires a better understanding of how the natural system (e.g., climate variability and change, extreme weather events, and processes affecting soil fertility) affects human processes. To capture and formalize our understanding of the interactions and feedback between human and natural systems a variety of modelling approaches are used. While integrated assessment models are widely recognized as supporting this goal and integrating representations of the human and natural system for global applications, an increasing diversity of models and corresponding research have focused on coupling models specializing in specific human (e.g., decision-making) or natural (e.g., erosion) processes at multiple scales. Domain experts develop these specialized models with a greater degree of detail, accuracy, and transparency, with many adopting open-science norms that use new technology for model sharing, coupling, and high performance computing. We highlight examples of four different approaches used to couple representations of the human and natural system, which vary in the processes represented and in the scale of their application. The examples illustrate how groups of researchers have attempted to overcome the lack of suitable frameworks for coupling human and natural systems to answer questions specific to feedbacks between human and natural systems. We draw from these examples broader lessons about system and model coupling and discuss the challenges associated with maintaining consistency across models and representing feedback between human and natural systems in coupled models.