With the rapid development of satellite remote sensing technology, carbon-cycle research, as a key focus of global climate change, has also been widely developed in terms of carbon source/sink-research methods. The internationally recognized “top-down” approach, which is based on satellite observations, is an important means to verify greenhouse gas-emission inventories. This article reviews the principles, categories, and development of satellite detection payloads for greenhouse gases and introduces inversion algorithms and datasets for satellite remote sensing of XCO2. It emphasizes inversion methods based on machine learning and assimilation algorithms. Additionally, it presents the technology and achievements of carbon-assimilation systems used to estimate carbon fluxes. Finally, the article summarizes and prospects the future development of carbon-assimilation inversion to improve the accuracy of estimating and monitoring Earth’s carbon-cycle processes.