The main roles of fault detection and diagnosis (FDD) for industrial processes are to make an effective indicator which can identify faulty status of a process and then to take a proper action against a future failure or unfavorable accidents. In order to enhance many process performances (e.g., quality and throughput), FDD has attracted great attention from various industrial sectors. Many traditional FDD techniques have been developed for checking the existence of a trend or pattern in the process or whether a certain process variable behaves normally or not. However, they might fail to produce several hidden characteristics of the process or fail to discover the faults in processes due to underlying process dynamics. In this paper, we present current research and developments of FDD approaches for process monitoring as well as a broad literature review of many useful FDD approaches.