Electronic devices have revolutionized society’s trajectories within, and interactions with, the world. The skin on our bodies holds incredible functionalities, such as stretchability and degradability, which only recently are being explored for electronic systems and have the potential to revolutionize device applications and disposal. Polymeric materials are especially poised to realize stretchable and transient electronics. In this article, strategies are reviewed for synthesizing and utilizing biodegradable and elastomeric organic materials, followed by component-specific materials approaches and examples of assembled stretchable and transient systems. Stretchable and biodegradable organic electronic devices will call upon intersections of different fields, which promise to open up new frontiers for electronics in the biomedical, exploratory, sensory, and consumer electronics fields.