This book constitutes three challenges that were held in conjunction with the 23rd International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2020, in Lima, Peru, in October 2020*: the Anatomical Brain Barriers to Cancer Spread: Segmentation from CT and MR Images Challenge, the Learn2Reg Challenge, and the Thyroid Nodule Segmentation and Classification in Ultrasound Images Challenge.The 19 papers presented in this volume were carefully reviewed and selected form numerous submissions. The ABCs challenge aims to identify the best methods of segmenting brain structures that serve as barriers to the spread of brain cancers and structures to be spared from irradiation, for use in computer assisted target definition for glioma and radiotherapy plan optimization. The papers of the L2R challenge cover a wide spectrum of conventional and learning-based registration methods and often describe novel contributions. The main goal of the TN-SCUI challenge is to find automatic algorithms to accurately segment and classify the thyroid nodules in ultrasound images. *The challenges took place virtually due to the COVID-19 pandemic.