Background: Food fraud is described as a violation of food law, which is intentionally committed to get an economic or financial gain through the consumer's swindle resulting in multi-million business and posing a public health threat. The main fraudulent practices are mislabelling of composition, certificates of origin, health claims, and artificial increases in weight or volume caused by replacement, dilution, addition or removal of some ingredients. Hardly 68% of the food fraud violations are produced in animal and vegetable products with high fat content (27% meat, 13% fish, 11% oils, 10% dairy products, 4% nuts and seeds and 3% animal by-products) becoming a crucial issue for food processing industries. Scope and approach: The present review focuses on the main authentication techniques and methods employed to clarify the authenticity of both animal and vegetable fat food products emphasizing the importance of the use of robust and reliable analytical techniques combined with multivariate analyses. Key findings and conclusions: Targeted approaches, such as as chromatography and DNA-based methods, combined with multivariate analysis have shown high accuracy, sensitivity and selectivity, allowing the simultaneous evaluation of multiple analytes. In addition, non-target methods, such as those based on spectroscopic techniques, have been used to establish the geographic origin of food products with quick response, low cost, non-destructive character and also offering the possibility to be miniaturized.