With the advancements of generative artificial intelligence (GenAI) models, their capabilities are expanding significantly beyond content generation and the models are increasingly being used across diverse applications. Particularly, GenAI shows great potential in addressing challenges in the electric vehicle (EV) ecosystem ranging from charging management to cyber-attack prevention. In this paper, we specifically consider Internet of electric vehicles (IoEV) and we categorize GenAI for IoEV into four different layers namely, EV's battery layer, individual EV layer, smart grid layer, and security layer. We introduce various GenAI techniques used in each layer of IoEV applications. Subsequently, public datasets available for training the GenAI models are summarized. Finally, we provide recommendations for future directions. This survey not only categorizes the applications of GenAI in IoEV across different layers but also serves as a valuable resource for researchers and practitioners by highlighting the design and implementation challenges within each layer. Furthermore, it provides a roadmap for future research directions, enabling the development of more robust and efficient IoEV systems through the integration of advanced GenAI techniques.

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