Elastomers are suitable materials for constructing a conformal interface with soft and curvilinear biological tissue due to their intrinsically deformable mechanical properties. Intrinsically soft electronic devices whose mechanical properties are comparable to human tissue can be fabricated using suitably functionalized elastomers. This article reviews recent progress in functionalized elastomers and their application to intrinsically soft and biointegrated electronics. Elastomers can be functionalized by adding appropriate fillers, either nanoscale materials or polymers. Conducting or semiconducting elastomers synthesized and/or processed with these materials can be applied to the fabrication of soft biointegrated electronic devices. For facile integration of soft electronics with the human body, additional functionalization strategies can be employed to improve adhesive or autonomous healing properties. Recently, device components for intrinsically soft and biointegrated electronics, including sensors, stimulators, power supply devices, displays, and transistors, have been developed. Herein, representative examples of these fully elastomeric device components are discussed. Finally, the remaining challenges and future outlooks for the field are presented.