Stereo depth estimation relies on optimal correspondence matching between pixels on epipolar lines in the left and right images to infer depth. In this work, we revisit the problem from a sequence-to-sequence correspondence perspective to replace cost volume construction with dense pixel matching using position information and attention. This approach, named STereo TRansformer (STTR), has several advantages: It 1) relaxes the limitation of a fixed disparity range, 2) identifies occluded regions and provides confidence estimates, and 3) imposes uniqueness constraints during the matching process. We report promising results on both synthetic and real-world datasets and demonstrate that STTR generalizes across different domains, even without fine-tuning.