Prolonging crops’ shelf-life while retaining their high quality is a major issue related to postharvest management. During storage, fruits and vegetables are exposed to microbial attacks, which may cause spoilage. Crop deterioration causes the loss of physical properties and drops in quality and nutritional value. Hence, new techniques to improve the resistance of food products are being explored. One promising technique is fumigation. Essential oils and their constituents, due to their antimicrobial properties, are likely to be used as fumigants, as they are highly volatile, effective in low concentrations, biodegradable, and safe. Papers indicate that some of them can improve their quality by increasing the content of antioxidants. This comprehensive review aims to present the current state of knowledge about the influence of essential oil fumigation on crop quality. It covers antioxidant capacity, the content of some bioactive compounds, physicochemical properties, decay properties, and sensory attributes of fruits and vegetables treated with essential oil vapors. The review indicates that this technique might be an interesting field for further exploration due to the promising results presented in the studies. Moreover, the review presents major objectives for current studies and indicates a lack of recent papers in this field.