Material advances in soft bioelectronics, particularly those based on stretchable nanocomposites─functional nanomaterials embedded in viscoelastic polymers with irreversible or reversible bonds─have driven significant progress in translational medical device research. The unique mechanical properties inherent in the stretchable nanocomposites enable stiffness matching between tissue and device, as well as its spontaneous mechanical adaptation to in vivo environments, minimizing undesired mechanical stress and inflammation responses. Furthermore, these properties allow percolative networks of conducting fillers in the nanocomposites to be sustained even under repetitive tensile/compressive stresses, leading to stable tissue-device interfacing. Here, we present an in-depth review of materials strategies, fabrication/integration techniques, device designs, applications, and translational opportunities of nanocomposite-based soft bioelectronics, which feature intrinsic stretchability, self-healability, tissue adhesion, and/or syringe injectability. Among many, applications to brain, heart, and peripheral nerves are predominantly discussed, and translational studies in certain domains such as neuromuscular and cardiovascular engineering are particularly highlighted.