Communication is one of the significant milestones of human beings; however, most of what we communicate is transmitted through facial expressions. Due to this, Facial Expression Recognition is one of the areas of most outstanding research in Artificial Intelligence for the potential benefits it can provide both economically and socially in areas such as marketing, education, security, technology, entertainment, politics, human resource management, or physical and mental health. This paper presents a review with the result of the comparative analysis of the main advances in the challenges that the identification of emotions entails, presenting the conceptual architecture model of each solution. It describes the praxis of how machine learning, artificial neural networks, deep learning, optimization algorithms, metaheuristics, and even anatomy and psychology tools—such as Action Units and the Arousal-Valence Two-Dimensional Model—drive the development of this transcendent area.