This chapter provides an overview of the main multiway methods used for data decomposition, calibration and pattern recognition. Parallel factor analysis (PARAFAC), PARAFAC2, Tucker3 and other multiway methods are briefly presented, together with a description and discussion of the main properties and steps of their most popular algorithms. The theoretical explanation is accompanied by some illustrative examples of their application in the field of Food Science (classification of vinegars with Excitation-Emission Fluorescence, ripening of apples measured with GC–MS, sensory analysis and prediction of sugar properties based on fluorescence landscape).