This review provides insight into consumer attitudes toward functional food (FF), with the purpose of better understanding the needs and behavior regarding this kind of product. A total of 47 articles were selected for this paper. The available studies from last 20 years differ according to the focus (awareness, attitudes, motivations, willingness, acceptance by consumers) and methodologies used. Several factors, including socio-demographic, cognitive and attitudinal ones, seem to be serve as the basis for the acceptance of functional products. The research papers showed that nutritional knowledge is the most important of these. Older people are more interested in functional products than younger consumers, because of their stronger belief in the health benefits of FF. Moreover, women are more open to compromise between taste and health properties. Claims concerning the disease preventative properties of FF are the most attractive for consumers. This review focuses also on future perspectives for the functional food market. Adequate knowledge and evidence-based communication seem to be the most promising ways to increase consumers’ interest in these kinds of products.