This chapter presents the most widely applied and, probably, satisfactory multivariate regression method used nowadays: partial least squares (PLS). Graphical explanations of many concepts are given to complement the more formal mathematical background. Several approaches to solving current problems are suggested. The development of a satisfactory regression model can alleviate the typical laboratory workload (preparation of many standards, solutions with concomitants, etc.) but only when a strict and serious job is performed with the PLS methodology. Iteration is the key word here as the analyst has to iterate the data within the software capabilities. Validation is essential, as can never be stressed sufficiently enough, and it will be explained here in detail. Two approaches to deal with the new concepts of ‘limit of detection’ and ‘limit of quantification’ (these terms will be used although they have been superseded) given by International Organization for Standardization (ISO) and the European Union (EU) are presented. Finally, a comprehensive review of practical applications that have used PLS within the atomic spectrometry field is presented.