In this paper, we present ECSIC, a novel learned method for stereo image compression. Our proposed method compresses the left and right images in a joint manner by exploiting the mutual information between the images of the stereo image pair using a novel stereo cross attention (SCA) module and two stereo context modules. The SCA module performs cross-attention restricted to the corresponding epipolar lines of the two images and processes them in parallel. The stereo context modules improve the entropy estimation of the second encoded image by using the first image as a context. We conduct an extensive ablation study demonstrating the effectiveness of the proposed modules and a comprehensive quantitative and qualitative comparison with existing methods. ECSIC achieves state-of-the-art performance in stereo image compression on the two popular stereo image datasets Cityscapes and InStereo2k while allowing for fast encoding and decoding.

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