Generative AI (GAI) has gained significant attention due to its powerful learning and generalization capabilities, and is increasingly applied in wireless communication scenarios. This paper discusses key applications of GAI in improving the performance of unmanned aerial vehicle (UAV) communication and networking. The paper first reviews key GAI technologies and the important roles of UAV networking. It then shows how GAI can enhance communication, networking, and security performance of UAV systems. A novel GAI framework for advanced UAV networking is proposed, and a case study on UAV-enabled spectrum map estimation and transmission rate optimization is presented to validate the effectiveness of GAI in UAV systems. The paper also discusses important open directions for future research. UAVs play critical roles in communications and networking, such as acting as relay stations, aerial base stations, edge computing devices, and attack detectors. However, traditional AI methods like discriminative AI (DAI) face challenges in handling UAV networking problems due to the mobility of UAVs and dynamic environments. GAI offers advantages such as data enhancement, latent space representation, and creativity, making it suitable for complex communication and networking optimization problems. GAI can be applied to UAV communications and networking at the physical, network, and application layers. At the physical layer, GAI can improve channel estimation and adaptive modulation. At the network layer, GAI can generate adaptive network topology management schemes. At the application layer, GAI can optimize resource allocation and task scheduling. Additionally, GAI can enhance physical layer security, detect anomalies, and preserve privacy in UAV networks. A case study is presented on UAV-enabled spectrum map estimation, where GAI is used to generate spectrum estimation maps based on UAV-collected data. The results show that GAI-based methods outperform traditional methods in accuracy and efficiency. The paper also discusses future directions for GAI in UAV communications and networks, including energy-efficient GAI, secure GAI, and multimodal processing. The study concludes that GAI has great potential to improve UAV communication and networking performance and highlights the importance of further research in this area.Generative AI (GAI) has gained significant attention due to its powerful learning and generalization capabilities, and is increasingly applied in wireless communication scenarios. This paper discusses key applications of GAI in improving the performance of unmanned aerial vehicle (UAV) communication and networking. The paper first reviews key GAI technologies and the important roles of UAV networking. It then shows how GAI can enhance communication, networking, and security performance of UAV systems. A novel GAI framework for advanced UAV networking is proposed, and a case study on UAV-enabled spectrum map estimation and transmission rate optimization is presented to validate the effectiveness of GAI in UAV systems. The paper also discusses important open directions for future research. UAVs play critical roles in communications and networking, such as acting as relay stations, aerial base stations, edge computing devices, and attack detectors. However, traditional AI methods like discriminative AI (DAI) face challenges in handling UAV networking problems due to the mobility of UAVs and dynamic environments. GAI offers advantages such as data enhancement, latent space representation, and creativity, making it suitable for complex communication and networking optimization problems. GAI can be applied to UAV communications and networking at the physical, network, and application layers. At the physical layer, GAI can improve channel estimation and adaptive modulation. At the network layer, GAI can generate adaptive network topology management schemes. At the application layer, GAI can optimize resource allocation and task scheduling. Additionally, GAI can enhance physical layer security, detect anomalies, and preserve privacy in UAV networks. A case study is presented on UAV-enabled spectrum map estimation, where GAI is used to generate spectrum estimation maps based on UAV-collected data. The results show that GAI-based methods outperform traditional methods in accuracy and efficiency. The paper also discusses future directions for GAI in UAV communications and networks, including energy-efficient GAI, secure GAI, and multimodal processing. The study concludes that GAI has great potential to improve UAV communication and networking performance and highlights the importance of further research in this area.