Deep learning models have achieved state-of-the-art performance in automated Cardiac Magnetic Resonance (CMR) analysis. However, the efficacy of these models is highly dependent on the availability of high-quality, artifact-free images. In clinical practice, CMR acquisitions are frequently degraded by respiratory motion, yet the robustness of deep learning models against such artifacts remains an underexplored problem. To promote research in this domain, we organized the MICCAI CMRxMotion challenge. We curated and publicly released a dataset of 320 CMR cine series from 40 healthy volunteers who performed specific breathing protocols to induce a controlled spectrum of motion artifacts. The challenge comprised two tasks: 1) automated image quality assessment to classify images based on motion severity, and 2) robust myocardial segmentation in the presence of motion artifacts. A total of 22 algorithms were submitted and evaluated on the two designated tasks. This paper presents a comprehensive overview of the challenge design and dataset, reports the evaluation results for the top-performing methods, and further investigates the impact of motion artifacts on five clinically relevant biomarkers. All resources and code are publicly available at: https://github.com/CMRxMotion