This paper provides a comprehensive survey on the applications, challenges, and opportunities of Generative AI (GAI) in unmanned vehicle swarms. It begins by introducing unmanned vehicles (UVs) and their types, including UAVs, UGVs, USVs, and UUVs, highlighting their use cases and existing issues. The paper then delves into the background of various GAI techniques, such as GANs, VAEs, GDMs, transformers, and normalizing flows, detailing their capabilities and advantages in enhancing UV swarms. It reviews the applications of GAI in state estimation, environmental perception, task/resource allocation, network coverage, and peer-to-peer communication, providing insights into how GAI addresses emerging problems in UV swarms. Finally, the paper highlights open issues and potential research directions in GAI for UV swarms, emphasizing the need for further development in areas like scalability, adaptive GAI, explainable swarm intelligence, security/privacy, and heterogeneous swarm intelligence. The contributions of the paper include a fundamental overview of UV swarms, an in-depth analysis of GAI techniques, a comprehensive review of GAI applications, and a discussion on future research directions.This paper provides a comprehensive survey on the applications, challenges, and opportunities of Generative AI (GAI) in unmanned vehicle swarms. It begins by introducing unmanned vehicles (UVs) and their types, including UAVs, UGVs, USVs, and UUVs, highlighting their use cases and existing issues. The paper then delves into the background of various GAI techniques, such as GANs, VAEs, GDMs, transformers, and normalizing flows, detailing their capabilities and advantages in enhancing UV swarms. It reviews the applications of GAI in state estimation, environmental perception, task/resource allocation, network coverage, and peer-to-peer communication, providing insights into how GAI addresses emerging problems in UV swarms. Finally, the paper highlights open issues and potential research directions in GAI for UV swarms, emphasizing the need for further development in areas like scalability, adaptive GAI, explainable swarm intelligence, security/privacy, and heterogeneous swarm intelligence. The contributions of the paper include a fundamental overview of UV swarms, an in-depth analysis of GAI techniques, a comprehensive review of GAI applications, and a discussion on future research directions.