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The precise maintenance and scientific management of large and complex mechanical equipment are of great significance for ensuring the safe operation of equipment and improving economic efficiency. Prognostics and health management (PHM), as an advanced method of equipment maintenance and management, has received widespread attention. Remaining useful life (RUL) prediction is one of the key technologies of PHM and has become a research hotspot and challenge in the field of equipment PHM. First, PHM and its key technology, i.e., RUL prediction (RULP), are briefly introduced. Its approaches are divided into statistical model-based approaches, artificial intelligence (AI) approaches, physics model-based approaches, and hybrid prognostic approaches. Then, the development branches and the current research status of each type of approach are sorted out, and the corresponding advantages and disadvantages are summarized. Finally, the future technological development direction and challenges faced are analyzed, providing some reference for the development and application of PHM in the future, as well as in-depth research on RULP approaches.