The advent of large language models (LLMs) such as BERT and, more recently, GPT, is transforming our approach of analyzing and understanding biomedical texts. To stay informed about the latest advancements in this area, there is a need for up-to-date summaries on the impact of LLM on Natural Language Processing (NLP) in the biomedical field. Thus, this scoping review aims to provide a detailed overview of the current state of biomedical NLP research and its applications, with a special focus on the evolving role of LLMs. We conducted a systematic search of PubMed, EMBASE, and Google Scholar for studies and conference proceedings published from 2017 to December 19, 2023, that develop or utilize LLMs for NLP tasks in biomedicine. From 13,823 references, we selected 199 publications and conference proceedings for our review. LLMs are being applied to a wide array of tasks in the biomedical field, including knowledge management, text mining, drug discovery, and evidence synthesis. Prominent among these tasks are text classification, relation extraction, and named entity recognition. Although BERT-based models remain prevalent, the use of GPT-based models has substantially increased since 2023.