This paper provides a comprehensive review of data-driven approaches for industrial process monitoring, covering historical development, current state-of-the-art, and future prospects. The review categorizes modeling techniques into multivariate statistics and machine learning, detailing principal component analysis (PCA), partial least squares (PLS), and artificial neural networks. It also examines process data exploration, treatment, software availability, and real-world industrial implementations. The paper discusses the evolution of process monitoring, from Shewhart's control charts to modern multivariate and machine learning methods. It highlights the importance of latent variable modeling in multivariate statistics and the role of machine learning in handling large datasets. The review includes detailed explanations of PCA, PLS, and CCA, their assumptions, and applications in fault detection and diagnosis. It also addresses challenges such as batch processes, dynamics, nonlinearity, multimodality, multiple time scales, and error handling. The paper concludes by discussing future research directions and the need for system performance, practical implementation, and benchmarking.This paper provides a comprehensive review of data-driven approaches for industrial process monitoring, covering historical development, current state-of-the-art, and future prospects. The review categorizes modeling techniques into multivariate statistics and machine learning, detailing principal component analysis (PCA), partial least squares (PLS), and artificial neural networks. It also examines process data exploration, treatment, software availability, and real-world industrial implementations. The paper discusses the evolution of process monitoring, from Shewhart's control charts to modern multivariate and machine learning methods. It highlights the importance of latent variable modeling in multivariate statistics and the role of machine learning in handling large datasets. The review includes detailed explanations of PCA, PLS, and CCA, their assumptions, and applications in fault detection and diagnosis. It also addresses challenges such as batch processes, dynamics, nonlinearity, multimodality, multiple time scales, and error handling. The paper concludes by discussing future research directions and the need for system performance, practical implementation, and benchmarking.