This book constitutes the refereed joint proceedings of the Third International Workshop on Reconstruction and Analysis of Moving Body Organs, RAMBO 2018, the Fourth International Workshop on Breast Image Analysis, BIA 2018, and the First International Workshop on Thoracic Image Analysis, TIA 2018, held in conjunction with the 21st International Conference on Medical Imaging and Computer-Assisted Intervention, MICCAI 2018, in Granada, Spain, in September 2018. The 5 full papers (out of 10 submissions) presented at RAMBO, the 9 full papers (out of 18 submissions) presented at BIA, and the 20 full papers (out of 21 submissions) presented at TIA were carefully reviewed and selected. The RAMBO papers cover aspects of medical imaging where motion plays a role in the image formation or analysis. The BIA papers deal with topics such as computer-aided detection and diagnosis of breast cancer, quantitative analysis of breast imaging modalities, and large scale breast image screening and analysis. The TIA papers cover aspects of image analysis research for lung and cardiac diseases including segmentation, registration, quantification, modeling of the image acquisition process, visualization, validation, statistical modeling, biophysical lung modeling (computational anatomy), deep learning and novel applications.