Satellite images are snapshots of the Earth surface. We propose to forecast them. We frame Earth surface forecasting as the task of predicting satellite imagery conditioned on future weather. EarthNet2021 is a large dataset suitable for training deep neural networks on the task. It contains Sentinel~2 satellite imagery at $20$~m resolution, matching topography and mesoscale ($1.28$~km) meteorological variables packaged into $32000$ samples. Additionally we frame EarthNet2021 as a challenge allowing for model intercomparison. Resulting forecasts will greatly improve ($>\times50$) over the spatial resolution found in numerical models. This allows localized impacts from extreme weather to be predicted, thus supporting downstream applications such as crop yield prediction, forest health assessments or biodiversity monitoring. Find data, code, and how to participate at www.earthnet.tech.