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Existing deep learning based stereo matching methods either focus on achieving optimal performances on the target dataset while with poor generalization for other datasets or focus on handling the cross-domain generalization by suppressing the domain sensitive features which results in a significant sacrifice on the performance. To tackle these problems, we propose PCW-Net, a Pyramid Combination and Warping cost volume-based network to achieve good performance on both cross-domain generalization and stereo matching accuracy on various benchmarks. In particular, our PCW-Net is designed for two purposes. First, we construct combination volumes on the upper levels of the pyramid and develop a cost volume fusion module to integrate them for initial disparity estimation. Multi-scale receptive fields can be covered by fusing multi-scale combination volumes, thus, domain-invariant features can be extracted. Second, we construct the warping volume at the last level of the pyramid for disparity refinement. The proposed warping volume can narrow down the residue searching range from the initial disparity searching range to a fine-grained one, which can dramatically alleviate the difficulty of the network to find the correct residue in an unconstrained residue searching space. When training on synthetic datasets and generalizing to unseen real datasets, our method shows strong cross-domain generalization and outperforms existing state-of-the-arts with a large margin. After fine-tuning on the real datasets, our method ranks first on KITTI 2012, second on KITTI 2015, and first on the Argoverse among all published methods as of 7, March 2022. The code will be available at https://github.com/gallenszl/PCWNet.