With the rapid development of artificial intelligence (AI), large language models (LLMs) have shown strong capabilities in natural language understanding, reasoning, and generation, attracting amounts of research interest in applying LLMs to health and medicine. Critical care medicine (CCM) provides diagnosis and treatment for critically ill patients who often require intensive monitoring and interventions in intensive care units (ICUs). Can LLMs be applied to CCM? Are LLMs just like stochastic parrots or ICU experts in assisting clinical decision-making? This scoping review aims to provide a panoramic portrait of the application of LLMs in CCM. Literature in seven databases, including PubMed, Embase, Scopus, Web of Science, CINAHL, IEEE Xplore, and ACM Digital Library, were searched from January 1, 2019, to June 10, 2024. Peer-reviewed journal and conference articles that discussed the application of LLMs in critical care settings were included. From an initial 619 articles, 24 were selected for final review. This review grouped applications of LLMs in CCM into three categories: clinical decision support, medical documentation and reporting, and medical education and doctor-patient communication. LLMs have advantages in handling unstructured data and do not require manual feature engineering. Meanwhile, applying LLMs to CCM faces challenges, including hallucinations, poor interpretability, bias and alignment challenges, and privacy and ethics issues. Future research should enhance model reliability and interpretability, integrate up-to-date medical knowledge, and strengthen privacy and ethical guidelines. As LLMs evolve, they could become key tools in CCM to help improve patient outcomes and optimize healthcare delivery. This study is the first review of LLMs in CCM, aiding researchers, clinicians, and policymakers to understand the current status and future potentials of LLMs in CCM.