Regulatory data compliance is a cornerstone of trust and accountability in critical sectors like finance, healthcare, and technology, yet its complexity poses significant challenges for organizations worldwide. Recent advances in natural language processing, particularly large language models, have demonstrated remarkable capabilities in text analysis and reasoning, offering promising solutions for automating compliance processes. This survey examines the current state of automated data compliance, analyzing key challenges and approaches across problem areas. We identify critical limitations in current datasets and techniques, including issues of adaptability, completeness, and trust. Looking ahead, we propose research directions to address these challenges, emphasizing standardized evaluation frameworks and balanced human-AI collaboration.