Wave energy converters (WECs) are a promising technology to contribute to the mix of renewable energies in the pursuit of a cleaner energy future. However, the demanding environment in which WECs operate presents a challenge from reliability and economic perspectives. There is a high likelihood of fault occurrence on WEC components, especially in offshore locations. While the control technology field can enhance energy extraction from WECs, any fault compromises the performance of the system and, in the worst case, can halt energy production, directly impacting revenue generation. Dealing with unexpected faults leads to more frequent maintenance operations, resulting in higher operational expenses. Similarly, strengthening WEC components to withstand harsh conditions comes with increased capital costs. Thus, fault management becomes crucial, whether it involves avoiding operation and maintenance (O&M) entirely or transitioning O&M to planned activities through a fault management mechanism (condition monitoring, fault-tolerant control, etc.), whereby the WEC maintains a certain level of system performance (or prevents emergency shutdown), eliminating the necessity for immediate intervention while still generating energy. In this regard, this study explores WEC components that are most likely to fail, also comprehensively covering WEC fault diagnosis, prognosis, condition monitoring and fault-tolerant control methods covered in the literature. Additionally, unexplored possibilities are pointed out, and future directions are suggested.