Emotional Intelligence (EI) refers to the ability to recognize, understand, and regulate emotions in oneself and others. With the rapid evolution of Artificial Intelligence (AI), researchers are increasingly exploring the integration of EI into machines to make them more adaptive, empathetic, and effective in human-cantered applications. This paper examines the concept of emotional intelligence, its relationship with AI, and the emerging field of affective computing. It highlights practical applications in healthcare, education, customer service, and mental health support, while also discussing ethical, social, and technical challenges. Finally, the paper concludes with future directions for building emotionally intelligent AI systems.