Generative AI (GenAI) is rapidly advancing the field of Autonomous Driving (AD), extending beyond traditional applications in text, image, and video generation. We explore how generative models can enhance automotive tasks, such as static map creation, dynamic scenario generation, trajectory forecasting, and vehicle motion planning. By examining multiple generative approaches ranging from Variational Autoencoder (VAEs) over Generative Adversarial Networks (GANs) and Invertible Neural Networks (INNs) to Generative Transformers (GTs) and Diffusion Models (DMs), we highlight and compare their capabilities and limitations for AD-specific applications. Additionally, we discuss hybrid methods integrating conventional techniques with generative approaches, and emphasize their improved adaptability and robustness. We also identify relevant datasets and outline open research questions to guide future developments in GenAI. Finally, we discuss three core challenges: safety, interpretability, and realtime capabilities, and present recommendations for image generation, dynamic scenario generation, and planning.