The excessive use or abuse of pesticides and veterinary drugs leads to residues in food, which can threaten human health. Therefore, there is an extremely urgent need for multi-analyte analysis techniques for the detection of pesticide and veterinary drug residues, which can be applied as screening techniques for food safety monitoring and detection. Recent developments related to rapid multi-residue detection methods for pesticide and veterinary drug residues are reviewed herein. Methods based on different recognition elements or the inherent characteristics of pesticides and veterinary drugs are described in detail. The preparation and application of three broadly specific recognition elements—antibodies, aptamers, and molecular imprinted polymers—are summarized. Furthermore, enzymatic inhibition-based sensors, near-infrared spectroscopy, and SERS spectroscopy based on the inherent characteristics are also discussed. The aim of this review is to provide a useful reference for the further development of rapid multi-analyte analysis of pesticide and veterinary drug residues.