Neurosymbolic AI combines neural network adaptability with symbolic reasoning, promising an approach to address the complex regulatory, operational, and safety challenges in Advanced Air Mobility (AAM). This survey reviews its applications across key AAM domains such as demand forecasting, aircraft design, and real-time air traffic management. Our analysis reveals a fragmented research landscape where methodologies, including Neurosymbolic Reinforcement Learning, have shown potential for dynamic optimization but still face hurdles in scalability, robustness, and compliance with aviation standards. We classify current advancements, present relevant case studies, and outline future research directions aimed at integrating these approaches into reliable, transparent AAM systems. By linking advanced AI techniques with AAM's operational demands, this work provides a concise roadmap for researchers and practitioners developing next-generation air mobility solutions.