Fundamental Capabilities and Applications of Large Language Models: A Survey

Large Language Models (LLMs) have demonstrated remarkable effectiveness across various domain-specific applications. However, which fundamental capabilities most contribute to their success in different domains remains unclear. This uncertainty complicates LLM evaluation, as existing benchmark-based assessments often fail to capture their real-world performance, where the required capabilities may differ from those measured in the benchmarks. In this survey, we provide a systematic introduction to LLMs’ fundamental capabilities, encompassing their definitions, formation mechanisms, and practical applications. We further explore the relationships among these capabilities and discuss how they collectively support complex problem-solving in domain-specific applications. Building on this foundation, we review recent advances in LLM-driven applications across nine specific domains: medicine, law, computational biology, finance, social sciences and psychology, computer programming and software engineering, robots and agents, AI for disciplines, and creative work. We analyze how specific capabilities are leveraged for each domain to address unique requirements. This perspective enables us to establish connections between these capabilities and domain requirements, and to evaluate the varying importance of different capabilities across different domains. Based on these insights, we propose evaluation strategies tailored to the essential capabilities required in each domain, offering practical guidance for selecting suitable backbone LLMs in real-world applications.