GUI agents, powered by large foundation models, can interact with digital interfaces, enabling various applications in web automation, mobile navigation, and software testing. However, their increasing autonomy has raised critical concerns about their security, privacy, and safety. This survey examines the trustworthiness of GUI agents in five critical dimensions: security vulnerabilities, reliability in dynamic environments, transparency and explainability, ethical considerations, and evaluation methodologies. We also identify major challenges such as vulnerability to adversarial attacks, cascading failure modes in sequential decision-making, and a lack of realistic evaluation benchmarks. These issues not only hinder real-world deployment but also call for comprehensive mitigation strategies beyond task success. As GUI agents become more widespread, establishing robust safety standards and responsible development practices is essential. This survey provides a foundation for advancing trustworthy GUI agents through systematic understanding and future research.