This paper presents neurosymbolic AI as a promising approach for solving complex regulatory, operational, and safety challenges in Advanced Air Mobility (AAM), examining applications in key AAM domains such as demand forecasting, aircraft design, and real-time air traffic management. While methodologies, including neurosymbolic reinforcement learning, demonstrate potential for dynamic optimization, we analyze challenges in scalability, robustness, and compliance with aviation standards. We categorize current progress, present relevant case studies, and suggest future research directions for integrating these approaches into reliable and transparent AAM systems. Finally, we provide a concise roadmap for developing next-generation air mobility solutions by connecting advanced AI technologies with the operational requirements of AAM.