Stereo matching recovers depth from image correspondences. Existing methods struggle to handle ill-posed regions with limited matching cues, such as occlusions and textureless areas. To address this, we propose MonSter, a novel method that leverages the complementary strengths of monocular depth estimation and stereo matching. MonSter integrates monocular depth and stereo matching into a dual-branch architecture to iteratively improve each other. Confidence-based guidance adaptively selects reliable stereo cues for monodepth scale-shift recovery, and utilizes explicit monocular depth priors to enhance stereo matching at ill-posed regions. Such iterative mutual enhancement enables MonSter to evolve monodepth priors from coarse object-level structures to pixel-level geometry, fully unlocking the potential of stereo matching. As shown in Fig.2, MonSter ranks 1st across five most commonly used leaderboards --- SceneFlow, KITTI 2012, KITTI 2015, Middlebury, and ETH3D. Achieving up to 49.5% improvements over the previous best method (Bad 1.0 on ETH3D). Comprehensive analysis verifies the effectiveness of MonSter in ill-posed regions. In terms of zero-shot generalization, MonSter significantly and consistently outperforms state-of-the-art methods across the board. Code will be released upon acceptance.