Recent advancements in model compression are focusing on enhancing the efficiency of large language models (LLMs) while maintaining their performance. Techniques such as adaptive pruning and family-aware quantization are gaining traction, addressing the challenges of computational cost and accuracy degradation. Adaptive pruning leverages an agent-guided approach to selectively prune layers, significantly improving factual knowledge retention and reducing perplexity without the need for retraining. Meanwhile, family-aware quantization regenerates calibration data to better capture activation distributions, leading to reduced accuracy loss during deployment. Additionally, new frameworks like Hessian Robust Quantization aim to stabilize low-bit quantization by reshaping the loss landscape, thus enhancing robustness against quantization noise. These developments are critical for deploying LLMs in resource-constrained environments, such as mobile devices and edge computing, where computational efficiency is paramount. The field is increasingly focused on creating methods that not only compress models but also ensure that they retain their essential capabilities, paving the way for more effective and practical applications.