The emergence of tools based on large language models (LLMs), like OpenAI’s ChatGPT and Google’s Gemini, has garnered immense public attention due to their advanced natural language generation capabilities. These remarkably natural-sounding tools have the potential to be highly useful across various tasks. However, they also tend to produce false, erroneous, or misleading content – commonly referred to as hallucinations. Additionally, LLMs can be misused to generate convincing yet false content and profiles on a large scale, posing a substantial societal challenge by potentially deceiving users and spreading inaccurate information. This makes fact-checking increasingly important. Despite their issues with factual accuracy, LLMs have shown proficiency in various subtasks that support fact-checking, which is essential for ensuring factually accurate responses. In light of these concerns, we explore the issues related to factuality in LLMs and their impact on fact-checking. We identify key challenges, imminent threats, and possible solutions to these factuality issues. We also thoroughly examine these challenges, existing solutions, and potential prospects for fact-checking. By analysing the factuality constraints within LLMs and their impact on fact-checking, we aim to contribute to a path towards maintaining accuracy at a time of confluence of generative AI and misinformation.