Causal discovery (CD) and Large Language Models (LLMs) represent two emerging fields of study with significant implications for artificial intelligence. Despite their distinct origins, CD focuses on uncovering cause-effect relationships from data, and LLMs on processing and generating humanlike text, the convergence of these domains offers novel insights and methodologies for understanding complex systems. This paper presents a comprehensive survey of the integration of LLMs, such as GPT4, into CD tasks. We systematically review and compare existing approaches that leverage LLMs for various CD tasks and highlight their innovative use of metadata and natural language to infer causal structures. Our analysis reveals the strengths and potential of LLMs in both enhancing traditional CD methods and as an imperfect expert, alongside the challenges and limitations inherent in current practices. Furthermore, we identify gaps in the literature and propose future research directions aimed at harnessing the full potential of LLMs in causality research. To our knowledge, this is the first survey to offer a unified and detailed examination of the synergy between LLMs and CD, setting the stage for future advancements in the field.