Recent high-level agreements such as the Paris Agreement and the Sustainable Development Goals aim at mitigating climate change, ecological degradation and biodiversity loss while pursuing social goals such as reducing hunger or poverty. Systemic approaches bridging natural and social sciences are required to support these agendas. The surging human use of biophysical resources (materials, energy) results from the pursuit of social and economic goals, while driving global environmental change. Sociometabolic research links the study of socioeconomic processes with biophysical processes and thus plays a pivotal role in understanding society–nature interactions. It includes a broad range of systems science approaches for measuring, analysing and modelling of biophysical stocks and flows as well as the services they provide to society. Here we outline and systematize major sociometabolic research traditions that study the biophysical basis of economic activity: urban metabolism, the multiscale integrated assessment of societal and ecosystem metabolism, biophysical economics, material and energy flow analysis, and environmentally extended input–output analysis. Examples from recent research demonstrate strengths and weaknesses of sociometabolic research. We discuss future research directions that could also help to enrich related fields. The United Nations Sustainable Development Goals and other high-level agreements acknowledge the linked nature of social and biophysical systems. This Review explains one research tradition, sociometabolic research, that explores these links. Sociometabolic research uses methods from systems science and allied areas to study the biophysical basis of economic activity. The authors use tangible examples from recent research to demonstrate strengths and weaknesses and then explore future directions.