This book constitutes the refereed proceedings of the Third MICCAI Workshop on Domain Adaptation and Representation Transfer, DART 2021, and the First MICCAI Workshop on Affordable Healthcare and AI for Resource Diverse Global Health, FAIR 2021, held in conjunction with MICCAI 2021, in September/October 2021. The workshops were planned to take place in Strasbourg, France, but were held virtually due to the COVID-19 pandemic. DART 2021 accepted 13 papers from the 21 submissions received. The workshop aims at creating a discussion forum to compare, evaluate, and discuss methodological advancements and ideas that can improve the applicability of machine learning (ML)/deep learning (DL) approaches to clinical setting by making them robust and consistent across different domains. For FAIR 2021, 10 papers from 17 submissions were accepted for publication. They focus on Image-to-Image Translation particularly for low-dose or low-resolution settings; Model Compactness and Compression; Domain Adaptation and Transfer Learning; Active, Continual and Meta-Learning.