This book constitutes the refereed proceedings of the Brain Tumor Segmentation Challenge, BraTS 2023, as well as the Cross-Modality Domain Adaptation Challenge, CrossMoDA 2023. These events were held in conjunction with the Medical Image Computing for Computer Assisted Intervention Conference, MICCAI 2023, during October 8-12, 2023. The 37 full papers presented in this volume were selected form 23 submissions. They describe the research of computational scientists and clinical researchers working on brain lesions, and specifically glioma, multiple sclerosis, cerebral stroke, traumatic brain injuries, vestibular schwannoma, and white matter hyper-intensities of presumed vascular origin.