Food authenticity, including edible oils and fats (EOFs), is an interesting issue since unethical players try to adulterate high priced EOFs with lower priced oils to gain the economical profits. Vibrational spectroscopy (VS) is considered a fingerprinting analytical tool capable of differentiating authentic and unauthentic fats and oils. Combined with multivariate data analysis or chemometrics, VS has been reported as the common method used for the authentication of EOFs. Chemometrics has been defined as the science providing the extraction of chemical data to get the maximum information employing statistics and mathematical methods. VS of EOFs involved very large chemical data and therefore the use of chemometrics is a must. The main objective of this review was to highlight the employment of VS in combination with chemometrics for the authentication of EOFs. In order to achieve this purpose, a search strategy using databases of SCOPUS, PubMed and DOAJ along with several keywords was carried out. VS such as Fourier transform infrared (FTIR), near infrared (NIR), and Raman spectroscopy in conjunction with chemometrics offered the most reliable outcome for the authentication analysis of EOFs. In addition, the combination of VS and chemometrics is a rapid and reliable analytical method with minimum sample preparation. Among those techniques, FTIR and NIR spectroscopy combined with chemometrics offer a more effective and efficient technique for the authentication of EOFs.