Large language models (LLMs) are increasingly applied to finance, yet challenges remain in aligning their capabilities with real-world institutional demands. In this survey, we provide a systematic, dual-perspective review bridging financial practice and LLM research. From a practitioner-centric standpoint, we introduce a functional taxonomy covering five core financial domains—Data Analysis, Investment Research, Trading, Investment Management, and Risk Management—mapping each to representative tasks, datasets, and institutional constraints. From a research-focused perspective, we analyze key modeling challenges, including numerical reasoning limitations, prompt sensitivity, and lack of real-time adaptability. We comprehensively catalog over 30 financial benchmarks and 20 representative models, and compare them across modalities, tasks, and deployment limitations. Finally, we identify open challenges and outline emerging directions such as continual adaptation, coordination-aware multi-agent systems, and privacy-compliant deployment. We emphasize deeper researcher–practitioner collaboration and transparent model architectures as critical pathways to safer and more scalable AI adoption in finance.