With the deep integration of artificial intelligence technology and wireless communication, semantic communication technology emerges as a vital mode focusing on semantic-level information transmission and interaction, thereby significantly enhancing communication accuracy and reliability. In the scenarios of low latency and high traffic density communication applications, semantic communication technology surpasses traditional syntactic-level communication grounded in classical information theory, presenting a new paradigm in wireless communication and expanding the application scope of modern communication technology. Nonetheless, the development of semantic communication technology is still in its infancy, and the security issues it faces in the application process have not been thoroughly researched and comprehensively analyzed. To advance the development and implementation of semantic communication technology, the paper first provides an overview of various security threats in semantic communication systems; then, it details the research status of model security and data security in semantic communication systems; finally, it summarizes the challenges and future trends in the security research of semantic communication.