Semantic communication allows the receiver to know the intention instead of the bit information itself, which is an emerging technique to support real-time human-machine and machine-to-machine interactions for future wireless communications. In semantic communications, both transmitter and receiver share some common knowledge, which can be used to extract small-size information at the transmitter and recover the original information at the receiver. Due to different design purposes, security issues in semantic communications have two unique features compared to standard bit-wise communications. First, an attacker in semantic communications considers not only the amount of stolen data but also the meanings of stolen data. Second, an attacker in semantic communication systems can attack not only semantic information transmission as done in standard communication systems but also attacks machine learning (ML) models used for semantic information extraction since most of semantic information is generated using ML based methods. Due to these unique features, in this paper, we present an overview on the fundamentals and key challenges in the design of secure semantic communication. We first provide various methods to define and extract semantic information. Then, we focus on secure semantic communication techniques in two areas: information security and semantic ML model security. For each area, we identify the main problems and challenges. Then, we will provide a comprehensive treatment of these problems. In a nutshell,this article provides a holistic set of guidelines on how to design secure semantic communication systems over real-world wireless communication networks.