This paper explores the advancements and applications of language models in healthcare, focusing on their clinical use cases. It examines the evolution from early encoder-based systems requiring extensive fine-tuning to state-of-the-art large language and multimodal models capable of integrating text and visual data through in-context learning. The analysis emphasizes locally deployable models, which enhance data privacy and operational autonomy, and their applications in tasks such as text generation, classification, information extraction, and conversational systems. The paper also highlights a structured organization of tasks and a tiered ethical approach, providing a valuable resource for researchers and practitioners, while discussing key challenges related to ethics, evaluation, and implementation.