<p>Terrestrial vegetation couples&#160;the global water, energy and carbon exchange between the atmosphere and the land surface. Thereby, vegetation productivity is determined by a multitude of energy- and water-related variables. While the emergent sensitivity of productivity to these variables has been inferred from Earth observations, its temporal evolution&#160;during the last decades is unclear, as well as potential changes in response to trends in hydro-climatic conditions.&#160;In this study, we analyze the changing sensitivity of global vegetation productivity to hydro-climate&#160;conditions by using satellite-observed vegetation indices&#160;(i.e. NDVI)&#160;at the monthly timescale from 1982&#8211;2015. Further, we&#160;repeat the analysis&#160;with simulated leaf area index and gross primary productivity from the TRENDY vegetation models, and contrast the findings with the observation-based results. We train a&#160;random forest model to predict anomalies of productivity from&#160;a comprehensive set of hydro-meteorological variables&#160;(temperature, solar radiation, vapor pressure deficit, surface and root-zone soil moisture and precipitation), and to infer the sensitivity to each of these variables. By&#160;training models from&#160;temporal independent subsets of the data we detect the evolution of sensitivity&#160;across time. Results based on observations&#160;show that vegetation sensitivity to energy- and water-related variables has significantly changed&#160;in many regions across the globe. In particular we find decreased (increased) sensitivity to temperature in very warm (cold) regions. Thereby, the magnitude of the sensitivity tends to differ between the early and late growing seasons. Likewise, we find changing sensitivity&#160;to root-zone soil moisture with increases predominantly in the early growing season and decreases in the late growing season.&#160;For better understanding the mechanisms behind the sensitivity changes, we analyse land-cover changes, hydro-climatic trends, and abrupt disturbances&#160;(e.g. drought, heatwave events or fires could result in breaking points of sensitivity evolution in the local interpretation). In summary, this study sheds light on how and where vegetation productivity changes&#160;its response to&#160;the drivers under&#160;climate change, which can help to understand possibly resulting&#160;changes in spatial and temporal patterns of land carbon uptake.</p>