The presence of some healthy phytochemicals in food can be paired with high bitterness, and consumers have a widespread avoidance toward bitter-tasting food. This causes a gap between preferences and healthy needs of consumers. Therefore, this review collected insights from literature belonging to different discipline domains in order to have a broad view of the current state-of-the-art about biochemical aspects and consumers’ perceptions and preferences toward foods with an enhanced bitter taste. In detail, we focused on two core products of the Mediterranean diet: Extra-virgin olive oil (EVOO) and Brassicaceae, both characterized by specific phytochemicals having strong healthy properties and bitter-pungent taste. Results suggested that, although bitter taste is a general driver of dislike, some exceptions can be represented by: niches of consumers (e.g., innovators and organic buyers), foods consumed with specific purposes (e.g., coffee, chocolate, and alcoholic beverages). The level of bitterness perceived by the consumers can be modulated through exposure, information on benefits, and elements within the environment (e.g., music). Thus, these insights can be used to develop specific campaigns aimed at promoting bitter (healthy) food, considering also the key role that could be played by food pairings.