Diamond nitrogen-vacancy (NV) center magnetometry has recently received considerable interest from researchers in the fields of applied physics and sensors. The purpose of this review is to analyze the principle, sensitivity, technical development potential, and application prospect of the diamond NV center magnetometry. This review briefly introduces the physical characteristics of NV centers, summarizes basic principles of the NV center magnetometer, analyzes the theoretical sensitivity, and discusses the impact of technical noise on the NV center magnetometer. Furthermore, the most critical technologies that affect the performance of the NV center magnetometer are described: diamond sample preparation, microwave manipulation, fluorescence collection, and laser excitation. The theoretical and technical crucial problems, potential solutions and research technical route are discussed. In addition, this review discusses the influence of technical noise under the conventional technical conditions and the actual sensitivity which is determined by the theoretical sensitivity and the technical noise. It is envisaged that the sensitivity that can be achieved through an optimized design is in the order of 10 fT/Hz^1/2. Finally, the roadmap of applications of the diamond NV center magnetometer are presented.