Autonomous driving systems (ADSs) have gained significant attention from both industry and academia due to their substantial economic, safety, and societal benefits, leading to in-depth research and the gradual popularization of applications. However, the introduction of such complex ecosystems can give rise to new safety issues that threaten the lives of pedestrians and impact the existing legal system. Therefore, it is imperative to validate ADSs through various methods such as simulation testing, access reviews, and pilot operations before the implementation and commercialization of ADSs. While the research on module safety has matured, there is still a lack of comprehensive research and organization regarding the safety of complete vehicle systems. Therefore, this study systematically analyzes vehicle system safety testing for ADSs and comprehensively reviews the current mainstream work. First, the architecture of ADSs and the basic procedure of simulation testing are outlined. The literature on vehicle system safety testing over the past six years is reviewed. Based on a universal testing framework, an autonomous driving safety testing framework tailored for vehicle systems is developed. Second, five core research issues are identified based on the aforementioned framework, namely critical scenario generation, test adequacy, adversarial sample generation, test optimization, and test oracle. A detailed analysis and organization of the key technologies, research status, and development context for each issue are provided. The commonly used evaluation metrics and comparative methods in current research are also summarized. Finally, the severe challenges faced by various research directions are summarized, and future research opportunities are anticipated, along with potential solutions.