The recent advancements in decentralized and hybrid parallel training frameworks for large-scale models have significantly enhanced the efficiency and scalability of deep learning systems. Researchers are focusing on addressing the challenges of stragglers, communication delays, and resource heterogeneity by introducing novel algorithms and system designs that optimize both computational and communication aspects. These innovations include adaptive compression techniques, decentralized training systems with geo-distributed GPUs, and straggler-resilient hybrid parallel training frameworks. The convergence of these approaches not only improves the accuracy and resource utilization but also reduces the training time and memory consumption, making large-scale model training more practical and accessible. Notably, the integration of decentralized training with adaptive compression and straggler mitigation strategies is proving to be a promising direction, offering substantial speedups and better generalization performance. These developments are crucial for advancing the field, especially in scenarios where hardware resources are limited or distributed across multiple nodes.