This chapter discusses partial least squares regression (PLS). The objective is to introduce newcomers to the most common procedures of this multivariate regression technique, explaining its advantages and limitations. As in the other chapters of the book, we will not focus only on the mathematics behind the method. Instead, we will present it graphically in an intuitive, pedagogic way, sufficient to understand the basis of the algorithm. Although the plots offer a simplified view of the method, they are good tools to visualize it even for those without a mathematical background. In this respect, it is worth stressing again that although spectroscopists act mainly as end users of the multivariate techniques, they should know the capabilities and limitations of the calibration techniques, in the same way as they master what is behind (for instance) the extraction method linked to a slurry sampling procedure. Advanced references will be given for readers who wish to seek a deeper understanding of this method. Throughout this chapter, the terms ‘instrumental response’, ‘independent variables’ or ‘predictors’ (this last term is the preferred one) denote the atomic spectra, whereas ‘dependent’, ‘predictand’ or ‘predicted variable’ (the second term is preferred) refer to concentration(s) of the analyte(s).