The demand for social robots in fields like healthcare, education, and entertainment increases due to their emotional adaptation features. These robots leverage multimodal communication, incorporating speech, facial expressions, and gestures to enhance user engagement and emotional support. The understanding of design paradigms of social robots is obstructed by the complexity of the system and the necessity to tune it to a specific task. This article provides a structured review of social robot design paradigms, categorizing them into cognitive architectures, role design models, linguistic models, communication flow, activity system models, and integrated design models. By breaking down the articles on social robot design and application based on these paradigms, we highlight the strengths and areas for improvement in current approaches. We further propose our original integrated design model that combines the most important aspects of the design of social robots. Our approach shows the importance of integrating operational, communicational, and emotional dimensions to create more adaptive and empathetic interactions between robots and humans.