Vegetation fires affect human infrastructures, ecosystems, global vegetation distribution, and atmospheric composition. In particular, extreme fire conditions can cause devastating impacts on ecosystems and human society and dominate the year-to-year variability in global fire emissions. However, the climatic, environmental and socioeconomic factors that control fire activity in vegetation are only poorly understood and consequently it is unclear which components, structures, and complexities are required in global vegetation/fire models to accurately predict fire activity at a global scale. Here we introduce the SOFIA (Satellite Observations for FIre Activity) modelling approach, which integrates several satellite and climate datasets and different empirical model structures to systematically identify required structural components in global vegetation/fire models to predict burned area. Models result in the highest performance in predicting the spatial patterns and temporal variability of burned area if they account for a direct suppression of fire activity at wet conditions and if they include a land cover-dependent suppression or allowance of fire activity by vegetation density and biomass. The use of new vegetation optical depth data from microwave satellite observations, a proxy for vegetation biomass and water content, reaches higher model performance than commonly used vegetation variables from optical sensors. The SOFIA approach implements and confirms conceptual models where fire activity follows a biomass gradient and is modulated by moisture conditions. The use of datasets on population density or socioeconomic development do not improve model performances, which indicates that the complex interactions of human fire usage and management cannot be realistically represented by such datasets. However, the best SOFIA models outperform a highly flexible machine learning approach and the state-of-the art global process-oriented vegetation/fire model JSBACH-SPITFIRE. Our results suggest using multiple observational datasets on climate, hydrological, vegetation, and socioeconomic variables together with model-data integration approaches to guide the future development of global process-oriented vegetation/fire models and to better understand the interactions between fire and hydrological, ecological, and atmospheric Earth system components.