The 2020 Multi-channel Magnetic Resonance Reconstruction (MC-MRRec) Challenge had two primary goals: 1) compare different MR image reconstruction models on a large dataset and 2) assess the generalizability of these models to datasets acquired with a different number of receiver coils (i.e., multiple channels). The challenge had two tracks: Track 01 focused on assessing models trained and tested with 12-channel data. Track 02 focused on assessing models trained with 12-channel data and tested on both 12-channel and 32-channel data. While the challenge is ongoing, here we describe the first edition of the challenge and summarise submissions received prior to 5 September 2020. Track 01 had five baseline models and received four independent submissions. Track 02 had two baseline models and received two independent submissions. This manuscript provides relevant comparative information on the current state-of-the-art of MR reconstruction and highlights the challenges of obtaining generalizable models that are required prior to clinical adoption. Both challenge tracks remain open and will provide an objective performance assessment for future submissions. Subsequent editions of the challenge are proposed to investigate new concepts and strategies, such as the integration of potentially available longitudinal information during the MR reconstruction process. An outline of the proposed second edition of the challenge is presented in this manuscript.