With the success and commercialization of 5G, 3GPP has started working toward the sixth generation of communication systems. While 5G explored the concept of non-terrestrial networks like satellites and unmanned aerial vehicles working alongside terrestrial networks, 6G is expected to take this integration a step further, aiming to achieve a more coherent network where satellites and terrestrial infrastructure work together seamlessly. However, the complexity and uniqueness of such networks create numerous attack surfaces that make them vulnerable to cyberattacks. The solution to such cyberattacks can be addressed by encryption and other upper-layer authentication methods. However, with the move to higher-frequency bands, such encryption techniques are difficult to scale for low-latency networks. In addition, the recent progress in quantum computing will make networks more vulnerable. To address such challenges, physical layer security (PLS) is proposed as a secure and quantum-resistant way to implement security by taking advantage of the physics of the channel and transceiver. This article reviews the latest trends and progress in PLS in integrated satellite–terrestrial networks (ISTNs) from a signal processing perspective. This work provides a comprehensive survey of the state-of-the-art research conducted, challenges, and future directions in the PLS of ISTNs.