Table Question Answering (TQA) aims to answer natural language questions about tabular data, often accompanied by additional contexts such as text passages. The task spans diverse settings, varying in table representation, question/answer complexity, modality involved, and domain. While recent advances in large language models (LLMs) have led to substantial progress in TQA, the field still lacks a systematic organization and understanding of task formulations, core challenges, and methodological trends, particularly in light of emerging research directions such as reinforcement learning. This survey addresses this gap by providing a comprehensive and structured overview of TQA research with a focus on LLM-based methods. We provide a comprehensive categorization of existing benchmarks and task setups. We group current modeling strategies according to the challenges they target, and analyze their strengths and limitations. Furthermore, we highlight underexplored but timely topics that have not been systematically covered in prior research. By unifying disparate research threads and identifying open problems, our survey offers a consolidated foundation for the TQA community, enabling a deeper understanding of the state of the art and guiding future developments in this rapidly evolving area.