Prognostics and health management (PHM) has become an essential function for safe system operation and scheduling economic maintenance. To date, there has been much research and publications on component-level prognostics. In practice, however, most industrial systems consist of multiple components that are interlinked. This paper aims to provide a review of approaches for system-level prognostics. To achieve this goal, the approaches are grouped into four categories: health index-based, component RUL-based, influenced component-based, and multiple failure mode-based prognostics. Issues of each approach are presented in terms of the target systems and employed algorithms. Two examples of PHM datasets are used to demonstrate how the system-level prognostics should be conducted. Challenges for practical system-level prognostics are also addressed.