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The terrestrial carbon cycle is an important component of global biogeochemical cycling and is closely related to human well-being and sustainable development. However, large uncertainties exist in carbon cycle simulations and observations. Model-data fusion is a powerful technique that combines models and observational data to minimize the uncertainties in terrestrial carbon cycle estimation. In this paper, we comprehensively overview the sources and characteristics of the uncertainties in terrestrial carbon cycle models and observations. We present the mathematical principles of two model-data fusion methods, i.e., data assimilation and parameter estimation, both of which essentially achieve the optimal fusion of a model with observational data while considering the respective errors in the model and in the observations. Based upon reviewing the progress in carbon cycle models and observation techniques in recent years, we have highlighted the major challenges in terrestrial carbon cycle model-data fusion research, such as the "equifinality" of models, the identifiability of model parameters, the estimation of representativeness errors in surface fluxes and remote sensing observations, the potential role of the posterior probability distribution of parameters obtained from sensitivity analysis in determining the error covariance matrixes of the models, and opportunities that emerge by assimilating new remote sensing observations, such as solar-induced chlorophyll fluorescence. It is also noted that the synthesis of multisource observations into a coherent carbon data assimilation system is by no means an easy task, yet a breakthrough in this bottleneck is a prerequisite for the development of a new generation of global carbon data assimilation systems. This article also highlights the importance of carbon cycle data assimilation systems to generate reliable and physically consistent terrestrial carbon cycle reanalysis data products with high spatial resolution and long-term time series. These products are critical to the accurate estimation of carbon cycles at the global and regional scales and will help future carbon management strategies meet the goals of carbon neutrality. [ABSTRACT FROM AUTHOR]