In chemometrics, the supervised and unsupervised classification of high-dimensional data has become a recurrent problem. Model-based techniques for discriminant analysis and clustering are popular tools, which are renowned for their probabilistic foundations and their flexibility. However, classical model-based techniques show a disappoint- ing behaviour in high-dimensional spaces, which up to now have been limited in their use within chemometrics. The recent developments in model-based classification overcame these drawbacks and enabled the efficient classifica- tion of high-dimensional data, even in the 'small n / large p' condition. This work presents a comprehensive review of these recent approaches, including regularization-based techniques, parsimonious modelling, subspace classifica- tion methods and classification methods based on variable selection. The use of these model-based methods is also illustrated on real-world classification problems in chemometrics using R packages.