A thin-film field-effect transistor (TFT) is a three-terminal device comprising source, drain, and gate electrodes, a dielectric layer, a semiconductor layer, and a substrate. The TFT is a fundamental building component in a variety of electronic devices. Developing an intrinsically stretchable TFT entails availability and usage of a functional material with elastomeric deformability in response to an externally applied stress. This represents a major materials challenge. In this article, we survey strategies to synthesize these elastomeric functional materials, and how these materials are assembled to fabricate intrinsically stretchable TFT devices. Developing solution-based printing technology to assemble intrinsically stretchable TFTs is considered a prospective strategy for wearable electronics for industrial adaptation in the near future.