This book constitutes the thoroughly refereed post-conference proceedings of the 4th International Workshop on Statistical Atlases and Computational Models of the Heart: Imaging and Modelling Challenges, STACOM 2013, held in conjunction with MICCAI 2013, in Nagoya, Japan, in September 2013. The 31 revised full papers were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on cardiac image processing; atlas construction; statistical modelling of cardiac function across different patient populations; cardiac mapping; 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.