• A systematic review of 175 studies on AI and LLM in aviation safety is presented. • Most studies focus on human factors, accident analysis, and operational safety. • The use of LLM in accident analysis and virtual copilots is surging. • Trustworthy and certified AI is the cornerstone for AI in aviation safety. • Hybrid intelligence design shall be considered for better human-AI teaming. The global air traffic is projected to grow significantly in the coming decades, leading to denser airspace and higher operational complexities. Therefore, academic and practitioners are now unleashing the potential of artificial intelligence (AI), particularly the recent advances in large language models (LLM), computer vision, and speech recognition in enhancing aviation safety through advanced cockpit design, AI assistants, human performance monitoring, and supporting air accident investigations. These applications demonstrate a significant promise in enhancing aviation safety. Nevertheless, there are still challenges in applying safe and reliable AI in supporting these safety–critical domains. Indeed, many aviation safety issues, such as accident analysis, human factors, and preventive system designs, are interconnected instead of standalone issues. This systematic literature review explores the recent advances, challenges, and future perspectives on leveraging AI to enhance aviation safety from a macro perspective. Therefore, a framework is established to review relevant studies. First, we identify the relevant literature from initial search, inspection, and screening. After that, we analyse the domains applied and the models leveraged in aviation safety enhancement on the 175 selected studies using content analysis. Then, thematic analysis is applied to reveal the challenges of applying safe and reliable AI in aviation safety. Given the challenges identified, this review recommends future work to incorporate explainable AI, develop AI certification frameworks, design based on hybrid intelligence, and adopt diversified dataset for generalisation.