The paper "Semantic Communication: A Survey of Its Theoretical Development" by Gangtao Xin, Pingyi Fan, and Khaled B. Letaief provides a comprehensive overview of the theoretical advancements in semantic communication. The authors highlight the growing demand for ultra-low latency and high-throughput capabilities in emerging intelligent services, which has driven significant interest in semantic communication. However, a comprehensive and effective theoretical framework for semantic communication remains elusive. The paper focuses on semantic information theory, which encompasses semantic entropy, semantic rate-distortion, and semantic channel capacity. It reviews the foundational work of Claude Shannon and presents recent developments in these areas, including the connection between Shannon's information theory and semantic information theory. The authors also discuss open problems in semantic information measurement and coding, and evaluate various mathematical theories and tools relevant to semantic communication. Additionally, they explore the challenges encountered in both semantic communication and semantic information theory, emphasizing the need for further research and development in this field. The paper is structured into several sections, covering the introduction to semantic communication, semantic entropy, semantic rate-distortion, semantic channel capacity, and related mathematical theories and tools.The paper "Semantic Communication: A Survey of Its Theoretical Development" by Gangtao Xin, Pingyi Fan, and Khaled B. Letaief provides a comprehensive overview of the theoretical advancements in semantic communication. The authors highlight the growing demand for ultra-low latency and high-throughput capabilities in emerging intelligent services, which has driven significant interest in semantic communication. However, a comprehensive and effective theoretical framework for semantic communication remains elusive. The paper focuses on semantic information theory, which encompasses semantic entropy, semantic rate-distortion, and semantic channel capacity. It reviews the foundational work of Claude Shannon and presents recent developments in these areas, including the connection between Shannon's information theory and semantic information theory. The authors also discuss open problems in semantic information measurement and coding, and evaluate various mathematical theories and tools relevant to semantic communication. Additionally, they explore the challenges encountered in both semantic communication and semantic information theory, emphasizing the need for further research and development in this field. The paper is structured into several sections, covering the introduction to semantic communication, semantic entropy, semantic rate-distortion, semantic channel capacity, and related mathematical theories and tools.