This paper presents a comprehensive review of data-driven approaches for industrial process monitoring. It covers the historical development, current state of the art, and future prospects of data-driven methods. The review critically evaluates various techniques, including multivariate statistics and machine learning. Key topics include process data exploration, software and benchmark availability, and real-world industrial implementations. The paper categorizes data-driven modeling techniques into multivariate statistics and machine learning, detailing representative models such as principal component analysis (PCA), partial least squares (PLS), and artificial neural networks. It also discusses the significance of these approaches, their performance, and development environments. The review aims to provide a reference for practitioners and researchers navigating the extensive literature on data-driven industrial process monitoring. The paper is structured into sections covering historical development, mathematical modeling techniques, process data exploration, computational tools, practical implementation, future perspectives, and a conclusion. Appendices provide additional resources for further exploration. The review highlights the importance of latent variable modeling in process monitoring and discusses the evolution of multivariate statistical techniques, including PCA, PLS, and CCA, as well as their applications in fault detection and diagnosis. It also addresses challenges such as nonlinearity, dynamics, multimodality, and poor data quality, and discusses recent trends and advancements in the field.This paper presents a comprehensive review of data-driven approaches for industrial process monitoring. It covers the historical development, current state of the art, and future prospects of data-driven methods. The review critically evaluates various techniques, including multivariate statistics and machine learning. Key topics include process data exploration, software and benchmark availability, and real-world industrial implementations. The paper categorizes data-driven modeling techniques into multivariate statistics and machine learning, detailing representative models such as principal component analysis (PCA), partial least squares (PLS), and artificial neural networks. It also discusses the significance of these approaches, their performance, and development environments. The review aims to provide a reference for practitioners and researchers navigating the extensive literature on data-driven industrial process monitoring. The paper is structured into sections covering historical development, mathematical modeling techniques, process data exploration, computational tools, practical implementation, future perspectives, and a conclusion. Appendices provide additional resources for further exploration. The review highlights the importance of latent variable modeling in process monitoring and discusses the evolution of multivariate statistical techniques, including PCA, PLS, and CCA, as well as their applications in fault detection and diagnosis. It also addresses challenges such as nonlinearity, dynamics, multimodality, and poor data quality, and discusses recent trends and advancements in the field.