The increase in Earth observations from space in recent years supports improved quantification of carbon storage by terrestrial vegetation and fosters studies that relate satellite measurements to biomass retrieval algorithms. However, satellite observations are only indirectly related to the carbon stored by vegetation. While ground surveys provide biomass stock measurements to act as reference for training the models, they are sparsely distributed. Here, we addressed this problem by designing an algorithm that harnesses the interplay of satellite observations, modeling frameworks and field measurements, and generated global estimates of above-ground biomass (AGB) density that meet the requirements of the scientific community in terms of accuracy, spatial and temporal resolution. The design was adapted to the amount, type and spatial distribution of satellite data available around the year 2020. The retrieval algorithm estimated AGB annually by merging estimates derived from C- and L-band synthetic aperture radar (SAR) backscatter observations with a Water Cloud type of model and does not rely on AGB reference data at the same spatial scale as the SAR data. This model is integrated with functions relating to forest structural variables that were trained on spaceborne LiDAR observations and sub-national AGB statistics. The yearly estimates of AGB were successively harmonized using a cost function that minimizes spurious fluctuations arising from the moderate-to-weak sensitivity of the SAR backscatter to AGB. The spatial distribution of the AGB estimates was correctly reproduced when the retrieval model was correctly set. Over-predictions occasionally occurred in the low AGB range (< 50 Mg ha-1) and under-predictions in the high AGB range (> 300 Mg ha-1). These errors were a consequence of sometimes too strong generalizations made within the modeling framework to allow reliable retrieval worldwide at the expense of accuracy. The precision of the estimates was mostly between 30% and 80% relative to the estimated value. While the framework is well founded, it could be improved by incorporating additional satellite observations that capture structural properties of vegetation (e.g., from SAR interferometry, low-frequency SAR, or high-resolution observations), a dense network of regularly monitored high-quality forest biomass reference sites, and spatially more detailed characterization of all model parameters estimates to better reflect regional differences.