(1) Background: Extra virgin olive oil (EVOO) is responsible for a large part of many health benefits associated to Mediterranean diet as it is a fundamental ingredient of this diet. The peculiarities of this golden, highly valued product are in part due to the requirements that must be met to achieve this title, namely, it has to be obtained using exclusively mechanical procedures, its free acidity cannot be greater than 0.8%, it must not show sensory defects, and it has to possess a fruity taste. (2) Methods: All these characteristics are key factors to EVOO quality, thus the chemical composition of these many health-promoting compounds, such as unsaturated fatty acids (which are also the major compounds, especially oleic acid), as well as minor components such as tocopherols or phenolic compounds (which behave as natural antioxidants) must be preserved. (3) Results: Due to the presence of all these compounds, the daily consumption of EVOO entails health benefits such as cardioprotective, antioxidant, anti-inflammatory, anti-tumor properties or acting as regulator of the intestinal microbiota, among others. (4) Conclusions: Taking all together, conserving EVOO chemical composition is essential to preserve its properties, so it is worth to control certain factors during storage like exposure to light, temperature, oxygen presence or the chosen packaging material, to maintain its quality and extend its shelf-life until its consumption.