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In the past two decades, satellite gravimetry has been widely developed to map the mass distribution on the Earth system. It helps human beings to have a deeper understanding of the dynamic processes that occur on the Earth's surface (e.g., atmosphere, hydrosphere, ocean, and polar ice sheets). This paper reviews the development history of challenging minisatellite payload, gravity recovery and climate experiment, gravity field and steady-state ocean circulation explorer, and gravity recovery and climate experiment follow-on. We briefly describe the research progress and problems of these gravity satellite missions. In order to overcome the shortcomings of the gravity satellites mentioned above, international research institutions propose numerous plans and simulation analyses for the next generation gravity mission (NGGM). This paper sorts out the task concepts, expected accuracy, and status for 12 kinds of NGGM proposed by international agencies. In order to introduce NGGM more clearly and grasp its current progress, we divide NGGM into four categories according to constellation configuration and satellite payload technology, including Sharifi-type gravity satellite constellation, Bender-type gravity satellite constellation, Satellitelink gravity satellite constellation, and Cold-atom gravity satellite constellation. This paper aims to sort out and summarize the NGGM to grasp the progress at this stage and presents some future perspectives for NGGM. [ABSTRACT FROM AUTHOR]