Aromatic plants and their essential oils have shown beneficial effects on the cardiovascular system and, therefore, are potential raw materials in the development of functional foods. However, despite their undeniable potential, essential oils present several limitations that need to be addressed, such as stability, poor solubility, undesirable sensory effects, and low bioavailability. The present review provides a current state-of-the-art on the effects of volatile extracts obtained from aromatic plants on the cardiovascular system and focuses on major challenges that need to be addressed to increase their use in food products. Moreover, strategies underway to overcome these limitations are pointed out, thus anticipating a great appreciation of these extracts in the functional food industry.