Stereo matching achieves significant progress with iterative algorithms like RAFT-Stereo and IGEV-Stereo. However, these methods struggle in ill-posed regions with occlusions, textureless, or repetitive patterns, due to lacking global context and geometric information for effective iterative refinement. To enable the existing iterative approaches to incorporate global context, we propose the Global Regulation and Excitation via Attention Tuning (GREAT) framework which encompasses three attention modules. Specifically, Spatial Attention (SA) captures the global context within the spatial dimension, Matching Attention (MA) extracts global context along epipolar lines, and Volume Attention (VA) works in conjunction with SA and MA to construct a more robust cost-volume excited by global context and geometric details. To verify the universality and effectiveness of this framework, we integrate it into several representative iterative stereo-matching methods and validate it through extensive experiments, collectively denoted as GREAT-Stereo. This framework demonstrates superior performance in challenging ill-posed regions. Applied to IGEV-Stereo, among all published methods, our GREAT-IGEV ranks first on the Scene Flow test set, KITTI 2015, and ETH3D leaderboards, and achieves second on the Middlebury benchmark. Code for reproducibility will be available in the future.