With the increasing demand for intelligent services, the sixth-generation (6G) wireless networks will shift from a traditional architecture that focuses solely on high transmission rate to a new architecture that is based on the intelligent connection of everything. Semantic communication (SemCom), a revolutionary architecture that integrates user as well as application requirements and meaning of information into the data processing and transmission, is predicted to become a new core paradigm in 6G. While SemCom is expected to progress beyond the classical Shannon paradigm, several obstacles need to be overcome on the way to a SemCom-enabled smart wireless Internet. In this paper, we first highlight the motivations and compelling reasons of SemCom in 6G. Then, we outline the major 6G visions and key enabler techniques which lay the foundation of SemCom. Meanwhile, we highlight some benefits of SemCom-empowered 6G and present a SemCom-native 6G network architecture. Next, we show the evolution of SemCom from its introduction to classical SemCom related theory and modern AI-enabled SemCom. Following that, focusing on modern SemCom, we classify SemCom into three categories, i.e., semantic-oriented communication, goal-oriented communication, and semantic-aware communication, and introduce three types of semantic metrics. We then discuss the applications, the challenges and technologies related to semantics and communication. Finally, we introduce future research opportunities. In a nutshell, this paper investigates the fundamentals of SemCom, its applications in 6G networks, and the existing challenges and open issues for further direction.