This book constitutes the proceedings of the International Workshop on Computational Diffusion MRI, CDMRI 2021, which was held on October 1, 2021, in conjunction with MICCAI 2021. The conference was planned to take place in Strasbourg, France, but was held virtually due to the COVID-19 pandemic. The 13 full papers included were carefully reviewed and selected for inclusion in the book. The proceedings also contain a paper about the design and scope of the MICCAI Diffusion-Simulated Connectivity Challenge (DiSCo) which was held at CDMRI 2021. The papers were organized in topical sections as follows: acquisition; microstructure modelling; tractography and connectivity; applications and visualization; DiSCo challenge – invited contribution.