Dealing with missing values in tabular data is a challenging task before proceeding to downstream applications such as model training. Various statistical and deep learning–based approaches have been applied to handle missing values in structured data, a process known as data imputation. With the rapid evolution of large language models (LLMs) for a variety of tasks, their performance and potential in tabular data imputation are also remarkable and worth exploring. This survey focuses exclusively on recent studies (2023–2025) that utilize LLMs for tabular data imputation. We categorize the various methodologies adopted to prepare LLMs for the imputation task and comprehensively discuss each of them. Additionally, we review numerous research works—highlighting their key characteristics, challenges, and research gaps and find out that LLMs provide better flexibility in handling mixed data types and context sensitive patterns where traditional methods struggle. We conclude by outlining promising directions for future research corresponding to each identified challenge and gap. To the best of our knowledge, while there are previous studies exploring LLMs for general data processing tasks, this is the first survey dedicated specifically to LLM-based tabular data imputation.