Olive oil, a fundamental component of the Mediterranean diet, is recognized as a functional food due to its health-promoting composition. The concentration of phenolic compounds in olive oil is influenced by various factors such as genetics, agro-climatic conditions, and technological processes. Therefore, to ensure an ideal intake of phenolics through the diet, it is recommended to produce functional enriched olive oil that contains a high concentration of bioactive compounds. The co-extraction technique is used to create innovative and differentiated products that promote the sensory and health-related composition of oils. To enrich olive oil, various natural sources of bioactive compounds can be used, including raw materials derived from the same olive tree such as olive leaves, as well as other compounds from plants and vegetables, such as herbs and spices (garlic, lemon, hot pepper, rosemary, thyme, and oregano). The development of functional enriched olive oils can contribute to the prevention of chronic diseases and improve consumers’ quality of life. This mini-review compiles and discusses relevant scientific information related to the development of enriched olive oil using the co-extraction technique and its positive effects on the health-related composition of oils.