The shelf life of fresh meat and fish is highly dependent on packaging technologies. The aim of any packaging system for fresh flesh foods is to prevent or delay undesirable changes to the appearance, flavour, odour, and texture. Moreover, microbial contamination, together with lipid and protein oxidation, are major concerns for meat and products thereof in terms of food safety. Modified atmosphere packaging (MAP) is widely applied in the packaging of both meat and fish. This packaging technology extends shelf life and improves appearance; however, several variables must be considered, such as temperature control and differences in gas compositions in combination with different types of meat. This review provides an overview of the available information on packaging technologies, from the perspectives of their characteristics, application types, and effects on the shelf life of poultry, meat, and fish. Special attention is paid to the MAP and active packaging.