Gravity measurements have important applications in geophysics, resource exploration, geodesy, and inertial navigation. The range of classical gravimetry includes laser interferometer (LI)-based absolute gravimeters, spring relative gravimeters, superconducting gravimeters, airborne/marine gravimeters, micro-electromechanical-system (MEMS) gravimeters, as well as gravity satellites and satellite altimetry. Atomic gravimetry is a new absolute gravity measurement technology based on atom interferometers (AIs) and features zero drift, long-term stability, long-term continuous measurements, and high precision. Atomic gravimetry has been used to measure static, marine, and airborne gravity; gravity gradient; as well as acceleration to test the weak equivalence principle at the China Space Station. In this paper, classical gravimetry is introduced, and the research progress on static and airborne/marine atomic gravimeters, space AIs, and atomic gravity gradiometers is reviewed. In addition, classical and atomic gravimetry are compared. Future atomic gravimetry development trends are also discussed with the aim of jointly promoting the further development of gravity measurement technologies alongside classical gravimetry.