Stereo image pairs encode 3D scene cues into stereo correspondences between the left and right images. To exploit 3D cues within stereo images, recent CNN based methods commonly use cost volume techniques to capture stereo correspondence over large disparities. However, since disparities can vary significantly for stereo cameras with different baselines, focal lengths and resolutions, the fixed maximum disparity used in cost volume techniques hinders them to handle different stereo image pairs with large disparity variations. In this paper, we propose a generic parallax-attention mechanism (PAM) to capture stereo correspondence regardless of disparity variations. Our PAM integrates epipolar constraints with attention mechanism to calculate feature similarities along the epipolar line to capture stereo correspondence. Based on our PAM, we propose a parallax-attention stereo matching network (PASMnet) and a parallax-attention stereo image super-resolution network (PASSRnet) for stereo matching and stereo image super-resolution tasks. Moreover, we introduce a new and large-scale dataset named Flickr1024 for stereo image super-resolution. Experimental results show that our PAM is generic and can effectively learn stereo correspondence under large disparity variations in an unsupervised manner. Comparative results show that our PASMnet and PASSRnet achieve the state-of-the-art performance.