This book constitutes the refereed proceedings of the 4th MICCAI Workshop on Domain Adaptation and Representation Transfer, DART 2022, held in conjunction with MICCAI 2022, in September 2022. DART 2022 accepted 13 papers from the 25 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.