Applications such as Earth science research, deep-space exploration, and geomagnetic navigation impose increasingly stringent requirements on the vector geomagnetic-field measurement performance of magnetometers. Magnetometers are required not only to possess both high sensitivity and a wide measurement range, but also to achieve high orthogonality to reduce errors in magnetic field direction measurement. Although traditional fluxgate magnetometers can perform geomagnetic measurements, their accuracy is limited. Superconducting quantum interference device (SQUID) magnetometers are constrained by measurement range, volume, and cryogenic operating conditions. In contrast, novel optical vector atomic magnetometers, with advantages such as high sensitivity, room-temperature operation, small size, and low power consumption, have become an important development direction for geomagnetic measurement technology. This paper presents a review of three mainstream vector atomic magnetometer schemes for geomagnetic measurements. Based on their operating mechanisms and functional characteristics, they are classified into three categories: vector schemes based on modulation and calculation with scalar atomic magnetometers (including coil-assisted and optical-control approaches), spin-exchange-relaxation-free (SERF) vector magnetometers, and diamond nitrogen-vacancy (NV) center vector magnetometers. This paper systematically describes the basic principles, domestic and international research status, and key advances of these three types of vector atomic magnetometers, and analyzes their respective characteristics in terms of sensitivity, measurement range, orthogonality control, and engineering maturity. Subsequently, the advantages, disadvantages, and performance specifications of the three schemes are compared, and it is further pointed out that measurement range and three-component orthogonality error are the core challenges commonly faced by all three schemes for practical geomagnetic measurement applications. Finally, future technological developments of three-axis vector atomic magnetometers for geomagnetic-field measurements are discussed.