Facial emotion recognition plays a vital role in enhancing human-computer interaction by allowing machines to perceive and react to human emotions. This paper conducts an in-depth exploration of various methodologies employed for recognizing facial emotions, emphasizing both traditional machine learning techniques and contemporary transfer learning models. We delve into a variety of algorithms such as support vector machines, and sophisticated neural networks like ResNet, EfficientNet, and MobileNet, assessing their efficacy using the standard MUG Facial Expression dataset. These models are tested to discern complex patterns in facial expressions, vital for accurate emotion detection. Our extensive analysis sheds light on the capabilities and constraints of each approach, providing valuable insights that pave the way for further research and practical deployments in this dynamic field. This comprehensive review aims to guide future advancements and enhance the practicality of facial emotion recognition systems.