Nanogenerators are a recently emerging technology which is able to cost-effectively harvest energy from renewable and clean energy sources at the micro/nano-scale. Their applications in the field of self-powered sensing systems and portable power supplying devices have been increasing in recent years. Wearable and implantable electromechanical/electrochemical transducers for energy harvesting represent a novel alternative to chemical batteries for low-power devices and to exploit the energy conveyed by human biomechanics. The human heart, in particular, is a compelling in vivo source of continuous biomechanical energy and is a natural battery which can power implantable or wearable medical devices. This review describes the recent advances in cardiac wearable/implantable soft and flexible devices and nanogenerators for energy harvesting (piezoelectric nanogenerators, triboelectric nanogenerators, biofuel cells, solar cells, etc.), as well as cardiovascular implantable electronic devices in a more general sense, as components of more complex self-sustainable bioelectronic systems for controlling irregular heartbeats or for interventional therapy for cardiac diseases. The main types of soft heart energy harvesters (HEHs) and heart bioelectronic systems (HBSs) are covered and classified, with a detailed presentation of state-of-the-art devices, and the advances in terms of materials choice, chemical functionalization, and design engineering are highlighted. In vivo bioelectronic cardiac interfaces are outlined as well as soft devices for in vitro cardiac models (patch and organoids). Cutting-edge 3D/4D bioprinting techniques of cardiac tissue are also mentioned. The technical challenges for the practical application and commercialization of soft HBSs are discussed at the end of this paper.