Semantic communication is emerging as the next pillar in wireless communication technology due to its transformative capabilities in reducing communication overhead, enhancing robustness, and enabling intelligent information exchange. The most significant obstacle lies in the lack of standardization across various research directions, leading to inconsistencies in interpretation, objectives, and evaluation. In this survey, we provide an in-depth overview of three leading directions in semantic communication, namely Theory of Mind-based semantic communication, Generative AI-driven semantic communication, and Deep Joint Source-Channel Coding (DJSCC)-based semantic communication. These directions have been extensively studied and developed by research institutes worldwide, and their effectiveness continues to improve alongside advances in communication and computing technologies. The ToM-based semantic communication enables communication agents to interact intelligently, infer each other's intentions, and gradually form a shared understanding. The GAI-based semantic communication leverages generative models to create and interpret content beyond traditional compression, allowing flexible semantic encoding and decoding tailored to specific tasks. The DJSCC-based semantic communication direction integrates DL models to jointly optimize the source and channel coding processes for efficient semantic information transfer. Next, we present a detailed survey of existing works under each direction and open research problems in semantic communication. Furthermore, we identify and analyze critical challenges, such as scalability and adaptability, that currently hinder the deployment of semantic communication systems. Finally, we discuss potential research opportunities and future directions such as quantum computing to further enhance the capabilities of semantic communication.