Background: Emotional Intelligence (EI) has become a key factor in educational environments, which facilitates and contributes to the mental well-being of teachers, and therefore, favours the teaching and learning process. However, education professionals are under constant stress. This stress is caused by a large number of social interactions, the new skills to be acquired, and the workload, developing in many situations the Burnout Syndrome (BS). Methods and Results: The study presents a systematic review, paying special attention to the scientific literature that combines IE and BS in the work performance of teachers as fundamental factors in the work carried out by educators at different educational stages, as well as the influence they have on the quality of the teaching-learning process. The Web of Science (WOS) has been used as a database, obtaining a total of 36 scientific articles intimately related to the topic of the work, published between 2005 and 2017. Many studies show that teachers are increasingly experiencing high feelings of stress, which affect the quality of education, as well as the relevance of developing emotional intelligence, which helps prevent these negative feelings from appearing. Conclusions: EI is a capacity that should be developed in teachers, since it gives the individual the ability to regulate his emotions, making him stronger in terms of decision-making in daily situations in the teaching environments, as well as being a key factor for the success of education. Through the positive reinforcement of EI, levels of stress and anxiety that worry society so much are reduced, since this avoids the feeling of frustration before their professional realisation, which leads to improved teaching practice, health and mental well-being of teachers.