Urban land use is often characterized based on the presence of built-up land, while the land use intensity of different locations is ignored. This narrow focus is at least partially due to a lack of data on the vertical dimension of urban land. The potential of Earth observation data to fill this gap has already been shown, but this has not yet been applied at large spatial scales. This study aims to map urban 3D building structure, i.e. building footprint, height, and volume, for Europe, the US, and China using random forest models. Our models perform well, as indicated by R2 values of 0.90 for building footprint, 0.81 for building height, and 0.88 for building volume, for all three case regions combined. In our multidimensional input variables, we find that built-up density derived from the Global Urban Footprint (GUF) is the most important variable for estimating building footprint, while backscatter intensity of Synthetic Aperture Radar (SAR) is the most important variable for estimating building height. A combination of the two is essential to estimate building volume. Our analysis further highlights the heterogeneity of 3D building structure across space. Specifically, buildings in China tend to be taller on average (10.35 m) compared to Europe (7.37 m) and the US (6.69 m). At the same time, the building volume per capita in China is lowest, with 302.3 m3 per capita, while Europe and the US show estimates of 404.6 m3 and 565.4 m3, respectively. The results of this study (3D building structure data for Europe, the US, and China) are publicly available, and can be used for further analysis of urban environment, spatial planning, and land use projections.