In fish, stressful events initiate a hormone cascade along the hypothalamus-pituitary-interrenal and hypothalamus-sympathetic-chromaffin (HSC) axis to evoke several physiological reactions in order to orchestrate and maintain homeostasis. Several biotic and abiotic factors, as well as aquaculture procedures (handling, transport, or stocking density), activated stress system inducing negative effects on different physiological processes in fish (growth, reproduction, and immunity). In order to reduce these consequences, the use of essential oils (EOs) derived from plants has been the focus of aquaculture studies due to their diverse properties (e.g., anesthetic, antioxidant, and antimicrobial), which have been shown to reduce biochemical and endocrine alterations and, consequently, to improve the welfare status. Recently, several studies have shown that biogenic compounds isolated from different EOs present excellent biological activities, as well as the nanoencapsulated form of these EOs may potentiate their effects. Overall, EOs presented less side effects than synthetic compounds, but their stress-reducing efficacy is related to their chemical composition, concentration or chemotype used. In addition, their species-specific actions must be clearly established since they can act as stressors by themselves if their concentrations and chemotypes used are not suitable. For this reason, it is necessary to assess the effect of these natural compound mixtures in different fish species, from marine to freshwater, in order to find the ideal concentration range and the way for their administration to obtain the desired biological activity, without any undesired side effects. In this review, the main findings regarding the use of different EOs as stress reducers will be presented to highlight the most important issues related to their use to improve fish welfare in aquaculture.