Vegetation attenuates the microwave emission from the land surface. The strength of this attenuation is quantified in models in terms of the parameter vegetation optical depth (VOD) and is influenced by the vegetation mass, structure, water content, and observation wavelength. Earth observation satellite sensors operating in the microwave frequencies are used for global VOD retrievals, enabling the monitoring of vegetation at large scales. VOD has been used to determine above-ground biomass, monitor phenology, or estimate vegetation water status. VOD can be also used for constraining land surface models or modelling wildfires at large scales. Several VOD products exist, differing by frequency/wavelength, sensor, and retrieval algorithm. Numerous studies present correlations or empirical functions between different VOD datasets and vegetation variables such as the normalized difference vegetation index, leaf area index, gross primary production, biomass, vegetation height, or vegetation water content. However, an assessment of the joint impact of land cover, vegetation biomass, leaf area, and moisture status on the VOD signal is challenging and has not yet been done. This study aims to interpret the VOD signal as a multi-variate function of several descriptive vegetation variables. The results will help to select VOD at the most suitable wavelength for specific applications and can guide the development of appropriate observation operators to integrate VOD with large-scale land surface models. Here we use VOD from the Land Parameter Retrieval Model (LPRM) in the Ku, X, and C bands from the harmonized Vegetation Optical Depth Climate Archive (VODCA) dataset and L-band VOD derived from Soil Moisture and Ocean Salinity (SMOS) and Soil Moisture Active Passive (SMAP) sensors. The leaf area index, live-fuel moisture content, above-ground biomass, and land cover are able to explain up to 93 % and 95 % of the variance (Nash-Sutcliffe model efficiency coefficient) in 8-daily and monthly VOD within a multi-variable random forest regression. Thereby, the regression reproduces spatial patterns of L-band VOD and spatial and temporal patterns of Ku-, X-, and C-band VOD. Analyses of accumulated local effects demonstrate that Ku-, X-, and C-band VOD are mostly sensitive to the leaf area index, and L-band VOD is most sensitive to above-ground biomass. However, for all VODs the global relationships with vegetation properties are non-monotonic and complex and differ with land cover type. This indicates that the use of simple global regressions to estimate single vegetation properties (e.g. above-ground biomass) from VOD is over-simplistic.