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The article discusses the use of latent variable models based on historical data and examines their potential and limitations for improving operations for both batch and continuous processes. The use of these models for multivariate statistical process monitoring, abnormal situation detection, and fault diagnosis is demonstrated. Examples from state-of-the-art major industrial applications currently running online illustrate the tremendous potential of these methods. In this context, an industrial application for abnormal situation detection is defined as "state of the art" if it has been operational several years after it was commissioned, has generated large savings, has been operating safely and/or has improved safety conditions in the plant, and is accepted enthusiastically by the operators. Such an application could be based entirely on known theory, but frequently it includes company proprietary modifications to suit the particular operating characteristics of the process. The article contains an extensive literature review on the subject and practical considerations for the user, as well as warnings about potential pitfalls in areas ranging from data acquisition to modeling to online application.