Space gravity gradiometry can resolve the medium-and short-wavelength components of the Earth′s gravity field. Spaceborne gravity gradiometers based on electrostatic accelerometers have played an important role in building global gravity field models. However, they still suffer from low-frequency measurement noise caused by factors such as the proof-mass structure, thermal environment, and satellite-platform disturbances. For instance, gravity field and steady-state ocean circulation explorer (GOCE)′s actual in-orbit low-frequency noise reached 24 mE/Hz. Benefiting from the space microgravity environment, spaceborne cold atom interferometry gravity gradiometers are expected to achieve a gravity gradient measurement precision far superior to that of ground-based instruments. Moreover, due to their characteristics of absolute gravity gradient measurement, they can compensate for the low-frequency noise and drift of electrostatic accelerometers, making them an important candidate payload for next-generation gravity gradiometry satellites. This paper reviews the parameter specifications of spaceborne electrostatic gravity gradiometers, the mechanisms and development history of ground-based atom interferometry gravity gradiometers, and the research status and future plans of spaceborne atom interferometers. This paper compares different spaceborne gravity gradiometer concepts, including European space agency cold atom gravity gradiometer (ESACGG), mass observation with cold atom sensors in space (MOCASS), quantum gravity gradiometer pathfinder (QGGPF), and a China′s proposed three-axis spaceborne gravity gradiometer, detailing their respective technical approaches. Through this comprehensive review, this paper summarizes the common design requirements of these schemes in terms of ultracold atom source temperature and long interrogation times, and delineate their specific design differences regarding interference mechanisms (Raman vs. Bragg) and measurement-axis orientations (radial vs. transverse). Meanwhile, taking the ESACGG scheme as an example, we outline its design parameters, payload specifications, satellite rotation stability, and other critical technical requirements and engineering issues under a target design sensitivity of 5 mE/Hz. Through this comprehensive review, we summarize the technical challenges and future development directions of spaceborne cold atom interferometry gravity gradiometers, providing a reference for the design of future gravity gradient projects based on spaceborne atom interferometry.