Stretchable electronics are highly attractive in various applications including wearable medical devices. However, most of the existing conducting materials used in electronics lack either high stretchability or high conductivity, largely limiting their applications. Inspired by the self-healing ability of skins, this project aims to develop next-generation conducting materials with combined high stretchability, high conductivity and intrinsic self-healing ability, based on novel graphene-supramolecular elastomer hybrids. The graphene-elastomer hybrids will be synthesised and investigated in depth for formulating the materials and obtaining a deep understanding of their mechanical, electrical and self-healing behaviour. Their application as stretchable electronics will be demonstrated by inkjet printing of the optimal material to form printed electrical circuits for wearable medical devices. These novel nanomaterials will significantly enhance the performance and lifetime of stretchable electronics as well as the design flexibility of future devices, whilst also facilitating the low-cost fabrication of electrical circuits through printing technologies.