Fires play an important role in the Earth system but remain complex phenomena that are challenging to model numerically. Here, we present the first version of BuRNN, a data-driven model simulating burned area on a global 0.5° × 0.5° grid with a monthly time resolution. We trained Long Short-Term Memory networks to predict satellite-based burned area (GFED5) from a range of climatic, vegetation and socio-economic parameters. We employed a region-based cross-validation strategy to account for the high spatial autocorrelation in our data. BuRNN outperforms the process-based fire models participating in ISIMIP3a on a global scale across a wide range of metrics. Regionally, BuRNN outperforms almost all models across a set of benchmarking metrics in all regions. However, in the African savannah regions and Australia burned area is underestimated, leading to a global underestimation of total area burned. Through eXplainable AI (XAI) we unravel the difference in regional drivers of burned area in our models, showing that the presence/absence of bare ground and C4 grasses along with the fire weather index have the largest effects on our predictions of burned area. Lastly, we used BuRNN to reconstruct global burned area for 1901–2019 and compare the simulations against independent long-term historical fire observation databases in five countries and the EU. Our approach highlights the potential of machine learning to improve burned area simulations and our understanding of past fire behaviour.