## 1 Introduction  
In recent years, consumers' attention towards the quality of foodstuff has become increasingly lively. The awareness that there exists a close link between health and diet has spread dramatically, leading a growing number of people to develop conscious eating habits. For this reason, and thanks to the so-called _food revolution_, aliments (especially high value-added food products) are commonly subjected to strict quality controls. These tests are of paramount importance, especially for attesting to some peculiar features (connected, for instance, to their geographical origin, their specific manufacturing process, and/or the know-how of their producers) that might translate into the recognition of distinctive labelling designations like the Protected Designation of Origin (PDO) or the Protected Geographical Indication (PGI). In light of this, a plethora of analytical methodologies aimed at foodstuff authentication and traceability have recently been developed, and a wide variety of applications of such methodologies have been reported in the scientific literature. More specifically, given the notable market value of this type of product, much effort has been put into the design of non-destructive characterization tools for quality control, generally based on the principles of light-matter interaction and spectroscopy. However, unfortunately, the signal profiles yielded by spectroscopy instrumentation (regardless of the spectral range investigated) are often particularly complex and thus, their assessment and interpretation are usually not straightforward. In this context, _multivariate statistical_ approaches (also known as _chemometric_ approaches) have lately played--and currently still play--a crucial role: they have proven, in fact, to be extremely powerful when large amounts of spectral data (characterized by a considerable degree of intercorrelation among the recorded spectral variables) need to be coped with, and when useful and meaningful information is to be extracted from these data for disparate purposes.  
Given, therefore, the sheer relevance of such approaches in the field of spectroscopy-based foodstuff analysis and authentication, this review aims at providing a comprehensive overview of those most commonly exploited in real-world case studies. Specifically, three scenarios will be here surveyed: exploration, calibration (necessary to carry out quantification) and classification (for, e.g., adulteration and/or fraud detection). The first one, intended to pursue direct insights into the data with the possibility of revealing hidden/underlying structures and relationships between samples and/or variables, and making extensive use of plots and graphs to highlight similarities, differences, trends, clusters and/or correlations, relies on so-called _unsupervised_ techniques, which do not require any input other than the (spectroscopic) data themselves [1]. On the other hand, calibration and classification problems call for the use of predictive models that exploit the spectroscopic information to predict one or more properties of the objects under study; in order to be reliable, such models have to be constructed by _supervised_ approaches, i.e., techniques which actively take advantage not only of the experimental (spectroscopic) data but also of, e.g., reference values of the aforementioned properties or sample labelling [2]. The main chemometric methodologies suited to addressing each one of these different tasks will be outlined, and examples illustrating their use will be provided alongside their description.