The underlying objective of food authentication studies is to determine whether unknown food samples have been correctly labelled. In this paper we study three near infrared (NIR) spectroscopic datasets from food samples of different types: meat samples (labelled by species), olive oil samples (labelled by their geographic origin) and honey samples (labelled as pure or adulterated by different adulterants). We apply and compare a large number of classification, dimension reduction and variable selection approaches to these datasets. NIR data pose specific challenges to classification and variable selection: the datasets are high - dimensional where the number of cases ($n$) $<<$ number of features ($p$) and the recorded features are highly serially correlated. In this paper we carry out comparative analysis of different approaches and find that partial least squares, a classic tool employed for these types of data, outperforms all the other approaches considered.