Short-packet communication is a key technology to support two emerging application scenarios in 5G and beyond 5G, massive machine type communication (mMTC) and ultra-reliable low latency communication (uRLLC), which are introduced to satisfy the broader communication requirements of potential applications such as the internet of vehicles and industrial internet of things (IoT). The sharp increase in privacy data in various IoT applications has made security issues more prominent. The typical upper-layer encryption mechanism could not fully address the security challenge considering the resource restriction of IoT terminals. In this article, we investigate secure short-packet communication from the perspective of physical layer security (PLS), which can be regarded as a promising security solution in 6G. Specifically, the state-of-the-art development of fundamental information theory of secure short-packet communications and corresponding performance evaluation criterion in fading channels are summarized. Then we review recent works, which investigate short-packet communication systems (CSs) in different communication scenarios or with different security strategies from the perspective of PLS. Finally, we give future research directions and challenges.