Recent advances in nanostructured materials and unconventional device designs have transformed the bioelectronics from a rigid and bulky form into a soft and ultrathin form and brought enormous advantages to the bioelectronics. For example, mechanical deformability of the soft bioelectronics and thus its conformal contact onto soft curved organs such as brain, heart, and skin have allowed researchers to measure high-quality biosignals, deliver real-time feedback treatments, and lower long-term side-effects in vivo. Here, we review various materials, fabrication methods, and device strategies for flexible and stretchable electronics, especially focusing on soft biointegrated electronics using nanomaterials and their composites. First, we summarize top-down material processing and bottom-up synthesis methods of various nanomaterials. Next, we discuss state-of-the-art technologies for intrinsically stretchable nanocomposites composed of nanostructured materials incorporated in elastomers or hydrogels. We also briefly discuss unconventional device design strategies for soft bioelectronics. Then individual device components for soft bioelectronics, such as biosensing, data storage, display, therapeutic stimulation, and power supply devices, are introduced. Afterward, representative application examples of the soft bioelectronics are described. A brief summary with a discussion on remaining challenges concludes the review.