Meat industries are constantly facing new waves of changes in the consumer’s nutritional trends, food safety, and quality requirements and legislations leading to an increase in interest for meat biopreservation to respond to all of these modern socioeconomic demands. Hence, to replace synthetic and/or expensive additives, new technologies in preserving meat products from microbial contamination have been established. In this context, organic acids and their salts have been considered as the most popular examples of preservatives that offer several advantages to be applied in meat industry. Here, characteristics of organic acids/salts commonly used in meat preservation were described based on the published literature. Moreover, after outlining the challenges and advantages of their use in meat industry, their current applications as meat preservatives on various meat type matrices such as beef, pork, sheep, and poultry were quite exposed based on previous and recent research works. Then, different application types were highlighted. Besides, some potent synergistic approaches based on several combinations of organic acids/salts with different existing preservative techniques are reported with an emphasised discussion of their application as possible solution tools to mainly overcome some problems linked to organic acids/salts when used solely, thus contributing to ensure the overall safety and improve the quality of meats. Finally, despite their usefulness in meat preservation, organic acids/salts may possess detrimental traits. In this context, a detailed discussion on their limits of use in meat products was provided in the last section of this paper.