•Instrumental analysis of food generates of a large volume of information per sample.•Discarding non-informative and/or redundant signals through variable selection.•A new categorization of the different variable selection strategies is presented.•Details about variable selection with applications in food analysis are shown.•Variable selection-based models have similar or better figures of merit. Food analysis covers aspects of quality and detection of possible frauds to ensure the integrity of the food. The arsenal of analytical instruments available for food analysis is broad and allows the generation of a large volume of information per sample. But this instrumental information may not yet give the desired answer; it must be processed to provide a final answer for decision making. The possibility of discarding non-informative and/or redundant signals can lead to models of better accuracy, robustness, and chemical interpretability, in line with the principle of parsimony. Thus, in this tutorial review, we cover aspects of variable selection in food analysis, including definitions, theoretical aspects of variable selection, and case studies showing the advantages of variable selection-based models concerning the use of a wide range of non-informative and redundant instrumental information in the analysis of food matrices.