Managing and conserving forest ecosystems in Europe and worldwide is an indispensable component of climate adaptation and climate change mitigation strategies. Precise and up-to-date information about the health and the carbon balance of forests are, hence, critical to assess the current state of forests, trigger appropriate countermeasures against forest loss, and develop improved management strategies. Advances in both Earth observation and artificial intelligence have paved the way for the automation of forest monitoring using satellite time series data, including optical, radar, and LiDAR measurements. The forest maps produced by today's approaches, however, are still often limited to coarse resolutions and/or to relatively small spatial areas. To overcome those limitations, the AI4Forest project brings together experts in artificial intelligence, applied mathematics, computer science, spatial remote sensing, and climate change. AI4Forest strives for both conceptually novel AI methods for forest monitoring as well as for scalable AI methods that allow to process large amounts of data efficiently and at low cost. The resulting techniques will facilitate the generation of detailed forest maps at a very high spatial and temporal resolution for the whole European continent and the entire world, including tree species identification, mortality and biomass carbon stocks changes down to the level of individual trees.