This book constitutes the thoroughly refereed post-workshop proceedings of the 10th International Workshop on Statistical Atlases and Computational Models of the Heart: Atrial Segmentation and LV Quantification Challenges, STACOM 2019, held in conjunction with MICCAI 2019, in Shenzhen, China, in October 2019.The 42 revised full workshop papers were carefully reviewed and selected from 76 submissions. The topics of the workshop included: cardiac imaging and image processing, machine learning applied to cardiac imaging and image analysis, atlas construction, statistical modelling of cardiac function across different patient populations, cardiac computational physiology, model customization, atlas based functional analysis, ontological schemata for data and results, integrated functional and structural analyses, as well as the pre-clinical and clinical applicability of these methods.