Tables are fundamental in domains such as finance, healthcare, and public administration, yet real-world table tasks often involve noise, structural heterogeneity, and semantic complexity--issues underexplored in existing research that primarily targets clean academic datasets. This survey focuses on LLM-based Table Agents, which aim to automate table-centric workflows by integrating preprocessing, reasoning, and domain adaptation. We define five core competencies--C1: Table Structure Understanding, C2: Table and Query Semantic Understanding, C3: Table Retrieval and Compression, C4: Executable Reasoning with Traceability, and C5: Cross-Domain Generalization--to analyze and compare current approaches. In addition, a detailed examination of the Text-to-SQL Agent reveals a performance gap between academic benchmarks and real-world scenarios, especially for open-source models. Finally, we provide actionable insights to improve the robustness, generalization, and efficiency of LLM-based Table Agents in practical settings.