Virgin olive oil, the main fat of the Mediterranean diet, is per se considered as a functional food—as stated by the European Food Safety Authority (EFSA)—due to its content in healthy compounds. The daily intake of endogenous bioactive phenolics from virgin olive oil is variable due to the influence of multiple agronomic and technological factors. Thus, a good strategy to ensure an optimal intake of polyphenols through habitual diet would be to produce enriched virgin olive oil with well-known bioactive polyphenols. Different sources of natural biological active substances can be potentially used to enrich virgin olive oil (e.g., raw materials derived from the same olive tree, mainly olive leaves and pomaces, and/or other compounds from plants and vegetables, mainly herbs and spices). The development of these functional olive oils may help in prevention of chronic diseases (such as cardiovascular diseases, immune frailty, ageing disorders and degenerative diseases) and improving the quality of life for many consumers reducing health care costs. In the present review, the most relevant scientific information related to the development of enriched virgin olive oil and their positive human health effects has been collected and discussed.