The emergence of deep learning has considerably advanced the state-of-the-art in cardiac magnetic resonance (CMR) segmentation. Many techniques have been proposed over the last few years, bringing the accuracy of automated segmentation close to human performance. However, these models have been all too often trained and validated using cardiac imaging samples from single clinical centres or homogeneous imaging protocols. This has prevented the development and validation of models that are generalizable across different clinical centres, imaging conditions or scanner vendors. To promote further research and scientific benchmarking in the field of generalizable deep learning for cardiac segmentation, this paper presents the results of the Multi-Centre, Multi-Vendor and Multi-Disease Cardiac Segmentation (M&Ms) Challenge, which was recently organized as part of the MICCAI 2020 Conference. A total of 14 teams submitted different solutions to the problem, combining various baseline models, data augmentation strategies, and domain adaptation techniques. The obtained results indicate the importance of intensity-driven data augmentation, as well as the need for further research to improve generalizability towards unseen scanner vendors or new imaging protocols. Furthermore, we present a new resource of 375 heterogeneous CMR datasets acquired by using four different scanner vendors in six hospitals and three different countries (Spain, Canada and Germany), which we provide as open-access for the community to enable future research in the field.