Fault detection and diagnosis for process plants has been an active area of research for many years. This review presents a concise overview on supervised and unsupervised data-driven approaches for fault detection and diagnosis in chemical processes. Methods based on supervised and unsupervised data-driven techniques are reviewed, and the challenges in the field of fault detection and diagnosis have also been highlighted. It is observed that most of the data-driven approaches are application specific, in that no single method can be used to obtain a generalized solution for nearly all purposes. The methods reviewed differ significantly from one to the other, and hence it is difficult to generalize any key similarity. The majority of the works proposed in the literature focused mainly on single fault detection, and do not cover the root-cause diagnosis of the detected faults. In cases where both detection and diagnosis are performed, the focus is mainly for a single fault. In addition, majority of the articles do not extend to the diagnosis of the root cause for multiple and simultaneous faults. © 2021 Wiley-VCH GmbH