Two approaches to monitoring the progress of batch processes are considered. The first approach based on nonlinear state estimation is reviewed and the problems in implementing it are discussed. A second approach based on multi-way principal components analysis can be developed directly from historical operating data. This approach leads to multivariate statistical process control plots which are very powerful in detecting subtle changes in process variable trajectories throughout the batch. This method is evaluated on a simulation of the semi-batch emulsion polymerization of styrene/butadiene.