Multivariate statistical procedures for monitoring the progress of batch processes are developed. The only information needed to exploit the procedures is a historical database of past successful batches. Multiway principal component analysis is used to extract the information in the multivariate trajectory data by projecting them onto low-dimensional spaces defined by the latent variables or principal components. This leads to simple monitoring charts, consistent with the philosophy of statistical process control, which are capable of tracking the progress of new batch runs and detecting the occurrence of observable upsets. The approach is contrasted with other approaches which use theoretical or knowledge-based models, and its potential is illustrated using a detailed simulation study of a semibatch reactor for the production of styrene-butadiene latex.