Various mechanical equipment play a crucial role, and their health or status may affect efficiency and safety seriously. Spectrum analysis of the corresponding signal has been widely used to diagnose the fault in the past decades. The diagnosis method based on spectrum analysis technology covers almost all aspects of mechanical fault diagnosis. However, there is a lack of review of diagnostic methods of spectrum analysis technologies in the field of mechanical equipment fault diagnosis. In order to fill this gap, this paper reviews the spectrum analysis technology in mechanical equipment diagnosis in detail. First of all, in order to let the researchers who are in contact with spectrum analysis technology for the first time quickly understand this field, the principles of spectrum are systematically sorted out, including spectrum, cepstrum, energy spectrum, power spectrum, higher-order spectrum, Hilbert spectrum, marginal spectrum, envelope spectrum, singular spectrum and so on. Furthermore, the characteristics of corresponding spectrum analysis technologies are summarized, and their advantages and disadvantages are analyzed and compared. High-quality references in recent ten years are cited for illustration to enhance persuasiveness. Finally, the prospect of spectrum analysis technology is summarized, and the future development trend of spectrum analysis technology is pointed out. It is believed that the joint diagnosis of fault severity, variable speed fault diagnosis, combined with deep learning and multiple spectrum analysis technologies should be given more attention in the future. This paper is expected to provide a comprehensive overview of mechanical fault diagnosis based on spectrum analysis theory, and help to develop corresponding spectrum analysis technologies in practical engineering.