Tables, typically two-dimensional and structured to store large amounts of data, are essential in daily activities like database queries, spreadsheet calculations, and generating reports from web tables. Automating these table-centric tasks with Large Language Models (LLMs) offers significant public benefits, garnering interest from academia and industry. This survey provides an extensive overview of table tasks, encompassing not only the traditional areas like table question answering (Table QA) and fact verification, but also newly emphasized aspects such as table manipulation and advanced table data analysis. Additionally, it goes beyond the early strategies of pre-training and fine-tuning small language models, to include recent paradigms in LLM usage. The focus here is particularly on instruction-tuning, prompting, and agent-based approaches within the realm of LLMs. Finally, we highlight several challenges, ranging from private deployment and efficient inference to the development of extensive benchmarks for table manipulation and advanced data analysis.
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