Materials used in wearable and implantable electronic devices should match the mechanical properties of biological tissues, which are inherently soft and deformable. In comparison to conventional rigid electronics, soft bioelectronics can provide accurate and real-time monitoring of physiological signals, improve comfort, and enable altogether new modalities for sensing. This article highlights recent progress, identifies technical challenges, and offers possible solutions for the emerging field of stretchable bioelectronics. We organize the content into three topical categories: (1) biological integration of soft electronic materials, (2) materials and mechanics, and (3) soft robotics. Finally, we conclude this article with a discussion on the outlook of the field and future challenges.