Prognostics and health management (PHM) has become an important component of many engineering systems and products, where algorithms are used to detect anomalies, diagnose faults and predict remaining useful lifetime (RUL). PHM can provide many advantages to users and maintainers. Although primary goals are to ensure the safety, provide state of the health and estimate RUL of the components and systems, there are also financial benefits such as operational and maintenance cost reductions and extended lifetime. This study aims at reviewing the current status of algorithms and methods used to underpin different existing PHM approaches. The focus is on providing a structured and comprehensive classification of the existing state-of-the-art PHM approaches, data-driven approaches and algorithms.