Chromatography has a very long history in the analysis of edible oils and fats. Hyphenations of two chromatographic methods, or couplings of a chromatographic separation technique with spectroscopic detection and identification devices, are used if the resolving power of the technique needs to be improved. More recently, the analytical benefits of comprehensive two-dimensional (2D) chromatography, in its various operational modes, have been exploited by the oil and fat chromatographic community. In comprehensive 2D chromatography, the entire sample injected is subjected to two independent separation processes. In the present contribution, the principles of comprehensive 2D chromatography are briefly discussed. Next, the advantages of comprehensive separations for lipid analysis are illustrated using the concept of generic chromatographic applications. This concept distinguishes three generic reasons to apply chromatographic separations: target compound analysis, group-type separation, and chromatographic fingerprinting. Examples of how comprehensive multi-dimensional methods were successfully applied to solve problems in the edible oils and fats area are given. We believe that these multi-dimensional techniques truly add new dimensions to oil and fat analysis, providing researchers in the area with novel tools for unraveling edible oil or fat samples with their complex compositions.