The presence of drug residues in food products has become a growing concern because of the adverse health risks and regulatory implications. Drug residues in food refer to the presence of pharmaceutical compounds or their metabolites in products such as meat, fish, eggs, poultry and ready-to-eat foods, which are intended for human consumption. These residues can come from the use of drugs in the field of veterinary medicine, such as antibiotics, antiparasitic agents, growth promoters and other veterinary drugs given to livestock and aquaculture with the aim of providing them as prophylaxis, therapy and for promoting growth. Various analytical techniques are used for this purpose to control the maximum residue limit. Compliance with the maximum residue limit is very important for food manufacturers according to the Food and Drug Administration (FDA) or European Union (EU) regulations. Effective monitoring and control of drug residues in food requires continuous advances in analytical techniques. Few studies have been reviewed on sample extraction and preparation techniques as well as challenges and future directions for the determination of veterinary drug residues in food. This current review focuses on the overview of regulations, classifications and types of food, as well as the latest analytical methods that have been used in recent years (2020–2023) for the determination of drug residues in food so that appropriate methods and accurate results can be used. The results show that chromatography is still a widely used technique for the determination of drug residue in food. Other approaches have been developed including immunoassay, biosensors, electrophoresis and molecular-based methods. This review provides a new development method that has been used to control veterinary drug residue limit in food.