Integrated satellite-terrestrial networks (ISTNs) are one of the new research directions for future 5G networks. Satellite coverage enables 5G communication throughout most of the world. However, the security concerns associated with the inherent broadcast nature of satellites are rarely considered. As an emerging security paradigm in 5G terrestrial communication, physical layer security (PLS) could have potential applications in an ISTN. This article describes the challenges of applying PLS to an ISTN, including correlated channels, co-channel interference, multiuserand multi-eavesdropper scenarios, and reliability concerns. The impacts of these challenges on the security performance of an ISTN and the corresponding solutions are analyzed for further comparison. Finally, we conclude the article by predicting future trends of PLS in an ISTN.