A global compilation of monthly and annual time-series of images for the periods 1982-2018 and 2000-2020 (data cube) is described. The prepared time-series for 1982-2018 (global at 5-km resolution) comprise: TerraClimate (Abatzoglou et al., 2018), vegetation monthly NDVI 90% percentiles for period 1982--2018 as a merge of the AVHRR daily and MODIS NDVI product, Vegetation Continuous Fields (VCF5KYR) Version 1 dataset (Song et al., 2018), Hyde v3.2 land use annual time-series (Klein Goldewijk et al., 2017), . For period 2000-2020 (global at 1-km resolution) MODIS land products (NDVI, LST, snow cover) in combination with MODIS atmospheric products (water vapour, cloud fraction), and global relief (MERIT DEM) and climate layers (CHELSA) are used. All layers have been resampled and gap-filled so they can be imported as an Analysis-Ready spatiotemporal array. For each pixel we also provide geometric temperatures (derived from latitude, day of the year and elevation) and for many layers also uncertainty measures. These datastacks have been made available via our OpenLandMap.org data portal and Cloud-Optimized GeoTIFF S3 file service and available for research and development. Overlaying Earth System Science point datasets (https://gitlab.com/openlandmap/compiled-ess-point-data-sets) such as the global compilation of soil organic carbon demonstrates that the global data cubes can be used to build complex spatiotemporal 2D+T models, including 3D+T, and produce predictions of important variables representing our dynamic environment. The two important advantages of running machine learning on spatiotemporal data recognized include: (1) possibility to explain complex casual relationships between environmental dynamics of plants, ecosystems communities, and soil variables and dynamic climate and human influence, (2) possibility to predict states beyond the time-span covered by training data - e.g. to predict future (as in scenario testing) and past states for which there are no training points.