We explore the integration of large language models (LLMs) into visual analytics (VA) systems to transform their capabilities through intuitive natural language interactions. We survey current research directions in this emerging field, examining how LLMs are integrated into data management, language interaction, visualisation generation, and language generation processes. We highlight the new possibilities that LLMs bring to VA, especially how they can change VA processes beyond the usual use cases. We especially highlight building new visualisation-language models, allowing access of a breadth of domain knowledge, multimodal interaction, and opportunities with guidance. Finally, we carefully consider the prominent challenges of using current LLMs in VA tasks. Our discussions in this paper aim to guide future researchers working on LLM-assisted VA systems and help them navigate common obstacles when developing these systems.