Cold plasma treatment is an innovative technology in the food processing and preservation sectors. It is primarily employed to deactivate microorganisms and enzymes without heat and chemical additives; hence, it is often termed a “clean and green” technology. However, food quality and safety challenges may arise during cold plasma processing due to potential chemical interactions between the plasma reactive species and food components. This review aims to consolidate and discuss data on the impact of cold plasma on the chemical constituents and physical and functional properties of major food products, including dairy, meat, nuts, fruits, vegetables, and grains. We emphasize how cold plasma induces chemical modification of key food components, such as water, proteins, lipids, carbohydrates, vitamins, polyphenols, and volatile organic compounds. Additionally, we discuss changes in color, pH, and organoleptic properties induced by cold plasma treatment and their correlation with chemical modification. Current studies demonstrate that reactive oxygen and nitrogen species in cold plasma oxidize proteins, lipids, and bioactive compounds upon direct contact with the food matrix. Reductions in nutrients and bioactive compounds, including polyunsaturated fatty acids, sugars, polyphenols, and vitamins, have been observed in dairy products, vegetables, fruits, and beverages following cold plasma treatment. Furthermore, structural alterations and the generation of volatile and non-volatile oxidation products were observed, impacting the color, flavor, and texture of food products. However, the effects on dry foods, such as seeds and nuts, are comparatively less pronounced. Overall, this review highlights the drawbacks, challenges, and opportunities associated with cold plasma treatment in food processing.