Semantic Communication is becoming the next pillar in wireless communication technology due to its various capabilities. However, it still encounters various challenging obstacles that need to be solved before real-world deployment. One of which is the lack of standardization across different directions, resulting in variations in interpretation and objectives. In the survey, we provide detailed explanations of three leading directions in semantic communications, namely Theory of Mind, Generative AI, Deep Joint Source-Channel Coding. These directions have been widely studied, developed, and verified by institutes worldwide, and their effectiveness has increased along with the advancement in technology. We first introduce the concepts and background of these directions in the survey. Firstly, the survey introduces the Theory of Mind, where the communication agents interact with each other, gaining understanding from observations and slowly forming a common language. Secondly, we present generative AI models, which can create new content and offer more freedom to interpret the data beyond the limitation of semantic meaning compression of raw data before transmitting it. Thirdly, our survey reviews deep learning models to jointly optimize the source and channel coding modules. Then, we present a comprehensive survey of existing works in each direction, thereby offering readers an overview of past achievements and potential avenues for further contribution. Moreover, for each direction, the survey identifies and discusses the existing challenges that must be addressed before these approaches can be effectively deployed in real-world scenarios. These challenges encompass a range of technical, computational, and practical issues in the survey. Finally, this survey also explores emerging trends such as specifically quantum computing, in semantic communication is discussed in this survey.

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