Model compression plays a crucial role in enabling the efficient and scalable deployment of deep learning models within environments constrained by latency and energy limits. This survey presents a unified taxonomy and introduces a deployment-aware framework that systematically organizes key compression strategies, including pruning, quantization, knowledge distillation, and low-rank decomposition, across the various stages of the training-to-deployment process. By combining both algorithmic and hardware perspectives, it addresses real-world deployment challenges such as latency variability across accelerators, restricted memory capacity, and irregular execution patterns, helping to achieve balanced trade-offs among compression ratio, accuracy, and runtime efficiency. Furthermore, by consolidating reproducible methodologies, standardized evaluation protocols, and benchmarking practices, this work provides a clear foundation and practical roadmap for researchers and practitioners to design, assess, and deploy compression methods effectively across diverse neural architectures in vision, language, speech, and multimodal domains. It emphasizes actionable guidance supported by theoretical understanding, aiming to bridge the gap between experimental efficiency improvements and the practical constraints of real-world deployment.