The gross primary production (GPP) of the terrestrial biosphere is a key source of variability in the global carbon cycle. It is modulated by hydrometeorological drivers (i.e., shortwave radiation, air temperature, vapor pressure deficit and soil moisture) and the vegetation state (i.e., canopy greenness, leaf area index) at instantaneous to interannual timescales. In this study, we set out to evaluate the ability of GPP-models to capture this variability. 11 models were considered, which rely purely on remote sensing data (RS-driven), meteorological data (meteo-driven, e.g., dynamic global vegetation models; DGVMs) or a combination of both (hybrid, e.g., light-use efficiency models; LUE). They were evaluated using in situ observations at 61 eddy covariance sites, covering a broad range of herbaceous and forest biomes. The results illustrated how the determinant of temporal variability shifts from meteorological variables at sub-seasonal timescales to biophysical variables at seasonal and interannual scale. RS-driven models lacked the sensitivity to the dominant drivers at short timescales (i.e., shortwave radiation and vapor pressure deficit), and failed to capture the decoupling of photosynthesis and canopy greenness (e.g., in evergreen forests). Conversely, meteo-driven models accurately captured the variability accross timescales, despite the challenges in the prognostic simulation of the vegetation state. Largest errors were found in water-limited sites, where the accuracy of the soil moisture dynamics determines the quality of the GPP estimates. In arid herbaceous sites, canopy greenness and photosynthesis were more tightly coupled, resulting in improved results with RS-driven models. Hybrid models capitalized on the combination of RS observations and meteorological information. LUE models were among the most accurate models to monitor GPP across all biomes, despite their simple architecture. Overall, we conclude that the combination of meteorological drivers and remote sensing observations is required to yield an accurate reproduction of the spatio-temporal variability of GPP. To further advance the performance of DGVMs, improvements in the soil moisture dynamics and vegetation evolution are needed.