As long as economic growth is a major political goal, decoupling growth from resource use and emissions is a prerequisite for a sustainable net-zero emissions future. However, empirical evidence for absolute decoupling, i.e. decreasing resource use and emissions at the required scale despite continued economic growth, is scarce and scattered across different research streams. In this two-part systematic review, we assess how and to what extent decoupling has been observed and what can be learnt for addressing the sustainability and climate crisis. Based on a transparent approach, we systematically identify and screen more than 11 500 scientific papers, eventually analyzing full texts of 835 empirical studies on the relationship between economic growth (GDP), resource use (materials and energy) and greenhouse gas emissions. Part I of the review examines how decoupling has been investigated across three research streams: energy, materials and energy, and emissions. Part II synthesizes the empirical evidence and policy implications (Haberl et al 2020 Environ. Res. Lett. 15 065003). In part I, we examine the topical, temporal and geographical scopes, methods of analysis, institutional networks and prevalent conceptual angles. We find that in this rapidly growing literature, the vast majority of studies—decomposition, 'causality' and Environmental Kuznets Curve analysis—approach the topic from a statistical-econometric point of view, while hardly acknowledging thermodynamic principles on the role of energy and materials for socio-economic activities. A potentially fundamental incompatibility between economic growth and systemic societal changes to address the climate crisis is rarely considered. We conclude that the existing wealth of empirical evidence merits braver conceptual advances than we have seen thus far.