As Generative AI (GenAI) continues to gain prominence and utility across various sectors, their integration into the realm of Internet of Things (IoT) security evolves rapidly. This work delves into an examination of the state-of-the-art literature and practical applications on how GenAI could improve and be applied in the security landscape of IoT. Our investigation aims to map the current state of GenAI implementation within IoT security, exploring their potential to fortify security measures further. Through the compilation, synthesis, and analysis of the latest advancements in GenAI technologies applied to IoT, this paper not only introduces fresh insights into the field, but also lays the groundwork for future research directions. It explains the prevailing challenges within IoT security, discusses the effectiveness of GenAI in addressing these issues, and identifies significant research gaps through MITRE Mitigations. Accompanied with three case studies, we provide a comprehensive overview of the progress and future prospects of GenAI applications in IoT security. This study serves as a foundational resource to improve IoT security through the innovative application of GenAI, thus contributing to the broader discourse on IoT security and technology integration.