The modern food market is undergoing a period of rapid development following the changes in marketing technologies and consumer behavior patterns. Nowadays, people pay more attention to the quality and composition of food products, as well as their functional properties. The present article reviews the international and Russian market of functional foods in order to define the consumer demand for new specialized products. The methods included data comparison, grouping, and systematization. The analysis involved Russian and foreign papers published in 2018–2022 and registered in Scopus, eLibrary, Cyberleninka, and the Library of the Russian Foundation for Basic Research. It also covered the National Demography Project, the Healthy Nutrition Project, and the Strategy for Improving the Quality of Food Products through 2030. Consumers’ growing interest in improving their health and immune system proved to be the key factor in the functional food market. The COVID-19 pandemic intensified such trends as the priority of healthy, high-protein, and low-sugar foods. Japan and the USA are the current leaders on this market. Russia supports healthy food policy at the state level. The functional food market is likely to become the most promising and competitive sector of global food economy. Consumer demand for these products is steadily growing: the volume of demand for functional food products will reach 17 trillion rubles by 2027. However, Russian food science needs more research in this area to catalyze import substitution. The Omsk Agrarian University has numerous projects that are meant to increase the competitiveness of the domestic functional food industry.