Adulteration of oils and fats is an important commercial issue, which needs intervention from regulatory agencies. Tremendous amount of research has been carried out during the past several decades to address this, starting from classical methods to more sophisticated instrumental techniques. Instrumental techniques based on chromatography and infrared spectroscopy have received particular attention from researchers worldwide since they are fast and efficient. Majority of the past studies suggested the use of assays based on fatty acids, triacylglycerol components, minor constituents, and spectral characteristics as they are really useful to determine the adulteration of food lipids. A discussion on the specificity and sensitivity of these assays in solving adulteration issues of oils and fats is timely. Hence, the purpose of this review is to present an update of the current literature in this topic and provide some directions for future research.