Reinforcement learning (RL)-based large language models (LLMs), such as ChatGPT, DeepSeek, and Grok-3, have gained significant attention for their exceptional capabilities in natural language processing and multimodal data understanding. Meanwhile, the rapid expansion of information services has driven the growing need for intelligence, efficient, and adaptable wireless networks. Wireless networks require the empowerment of RL-based LLMs while these models also benefit from wireless networks to broaden their application scenarios. Specifically, RL-based LLMs can enhance wireless communication systems through intelligent resource allocation, adaptive network optimization, and real-time decision-making. Conversely, wireless networks provide a vital infrastructure for the efficient training, deployment, and distributed inference of RL-based LLMs, especially in decentralized and edge computing environments. This mutual empowerment highlights the need for a deeper exploration of the interplay between these two domains. We first review recent advancements in wireless communications, highlighting the associated challenges and potential solutions. We then discuss the progress of RL-based LLMs, focusing on key technologies for LLM training, challenges, and potential solutions. Subsequently, we explore the mutual empowerment between these two fields, highlighting key motivations, open challenges, and potential solutions. Finally, we provide insights into future directions, applications, and their societal impact to further explore this intersection, paving the way for next-generation intelligent communication systems. Overall, this survey provides a comprehensive overview of the relationship between RL-based LLMs and wireless networks, offering a vision where these domains empower each other to drive innovations.