Large language models (LLMs) are being adopted quickly across biomedicine. Their value in clinical practice depends on more than accuracy: it also depends on whether they can run within the latency, hardware, privacy, cost, and staffing limits of real settings. In this scoping review of efficiency-oriented biomedical LLM research, we organize the literature along two axes: a taxonomy of efficiency techniques (prompting and retrieval, parameter-efficient and data-efficient adaptation, model compression, efficient architectures and inference, and agentic workflows) and a map of biomedical application domains. Across the corpus, prompting and parameter-efficient fine-tuning delivered efficiency most often, and studies reported it as savings in memory, trainable parameters, compute time, and human-workflow time, while energy and carbon were almost never measured. The reported gains are large and concrete: low-rank adaptation combined with low-precision quantization often shrinks the memory needed for adaptation enough to train and deploy a model on a single consumer or edge device, usually at a small and measured cost in task quality. Yet the evidence still leans toward retrospective benchmarking, with external validation, prospective evaluation, and clinical deployment all rare. We map which techniques serve which clinical domains, show how to read an efficiency claim against its comparator and clinical context, and identify what the field still needs to measure to turn demonstrated resource savings into validated clinical value.