In the fast-evolving domain of artificial intelligence, large language models (LLMs) such as GPT-3 and GPT-4 are revolutionizing the landscapes of finance, healthcare, and law: domains characterized by their reliance on professional expertise, challenging data acquisition, high-stakes, and stringent regulatory compliance. This survey offers a detailed exploration of the methodologies, applications, challenges, and forward-looking opportunities of LLMs within these high-stakes sectors. We highlight the instrumental role of LLMs in enhancing diagnostic and treatment methodologies in healthcare, innovating financial analytics, and refining legal interpretation and compliance strategies. Moreover, we critically examine the ethics for LLM applications in these fields, pointing out the existing ethical concerns and the need for transparent, fair, and robust AI systems that respect regulatory norms. By presenting a thorough review of current literature and practical applications, we showcase the transformative impact of LLMs, and outline the imperative for interdisciplinary cooperation, methodological advancements, and ethical vigilance. Through this lens, we aim to spark dialogue and inspire future research dedicated to maximizing the benefits of LLMs while mitigating their risks in these precision-dependent sectors. To facilitate future research on LLMs in these critical societal domains, we also initiate a reading list that tracks the latest advancements under this topic, which will be continually updated: \url{https://github.com/czyssrs/LLM_X_papers}.
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