Fault detection and diagnosis (FDD) systems are developed to characterize normal variations and detect abnormal changes in a process plant. It is always important for early detection and diagnosis, especially in chemical process systems to prevent process disruptions, shutdowns, or even process failures. However, there have been only limited reviews of data-driven FDD methods published in the literature. Therefore, the aim of this review is to provide the state-of-the-art reference for chemical engineers and to promote the application of data-driven FDD methods in chemical process systems. In general, there are two different groups of data-driven FDD methods: the multivariate statistical analysis and the machine learning approaches, which are widely accepted and applied in various industrial processes, including chemicals, pharmaceuticals, and polymers. Many different multivariate statistical analysis methods have been proposed in the literature, such as principal component analysis, partial least squares, independent component analysis, and Fisher discriminant analysis, while the machine learning approaches include artificial neural networks, neuro-fuzzy methods, support vector machine, Gaussian mixture model, K-nearest neighbor, and Bayesian network. In the first part, this review intends to provide a comprehensive literature review on applications of data-driven methods in FDD systems for chemical process systems. In addition, the hybrid FDD frameworks have also been reviewed by discussing the distinct advantages and various constraints, with some applications as examples. However, the choice for the data-driven FDD methods is not a straightforward issue. Thus, in the second part, this paper provides a guideline for selecting the best possible data-driven method for FDD systems based on their faults. Finally, future directions of data-driven FDD methods are summarized with the intent to expand the use for the process monitoring community.