Recently, the development of functional food products has played an essential role in healthy behavior. The increase in knowledge of consumers spurs concerns about health and how diet directly impacts health status. Functional foods are a new type of product that provide consumers with improvements in targeted physiological functions and a healthy lifestyle. Twenty-first-century consumers are seeking foods that have beneficial effects on the body beyond the conventional known nutritional role of the food. However, many consumers are still unclear about what functionality a given represents and the intended purpose of a given food product. In the Hungarian dairy sector, most dairy products stand out as the largest segment of functional foods giving the diversity of Hungarian’s functional dairy market. Several studies have looked at the trends of individual perception and consumer behavior regarding new foods in the market and their functional role in health and disease. The objective of this review is to highlight how health awareness influences the acceptance and consumption of dairy functional foods in Hungary.