This book constitutes the refereed joint proceedings of the 4th International Workshop on Interpretability of Machine Intelligence in Medical Image Computing, i MIMIC 2020, and the First International Workshop on Topological Data Analysis and Its Applications for Medical Data, TDA4Medical Data 2021, held on September 27, 2021, in conjunction with the 24th International Conference on Medical Imaging and Computer-Assisted Intervention, MICCAI 2021.The 7 full papers presented at i MIMIC 2021 and 5 full papers held at TDA4Medical Data 2021 were carefully reviewed and selected from 12 submissions each. The i MIMIC papers focus on introducing the challenges and opportunities related to the topic of interpretability of machine learning systems in the context of medical imaging and computer assisted intervention. TDA4Medical Data is focusing on using TDA techniques to enhance the performance, generalizability, efficiency, and explainability of the current methods applied to medical data.