The field of Large Language Models (LLMs) is moving towards more efficient and private fine-tuning methods, particularly in federated learning settings. Recent developments have focused on reducing communication costs, improving model adaptation, and mitigating non-IID data challenges. Notable advancements include novel low-rank adaptation techniques, adaptive federated fine-tuning frameworks, and sparse zeroth-order optimization methods. These innovations have demonstrated significant improvements in performance, efficiency, and robustness. Noteworthy papers include: SEMFED, which achieves an 80.5% reduction in communication costs while maintaining model accuracy above 98%. DenseLoRA, which enhances parameter efficiency and achieves superior performance compared to existing low-rank adaptation approaches. AFLoRA, which provides a practical solution for efficient LLM adaptation in heterogeneous environments. EcoLoRA, which significantly reduces communication overhead without compromising performance. PoLAR, which yields an exponentially faster convergence rate on a canonical low-rank adaptation problem. DiaBlo, which eliminates the need for low rank matrix products and achieves stable and robust convergence. Meerkat, which achieves remarkable communication efficiency and effectively mitigates Non-IID data challenges.