Stretchable polymer semiconductors have advanced rapidly in the past decade as materials required to realize conformable and soft skin-like electronics become available. Through rational molecular-level design, stretchable polymer semiconductor films are now able to retain their electrical functionalities even when subjected to repeated mechanical deformations. Furthermore, their charge-carrier mobilities are on par with the best flexible polymer semiconductors, with some even exceeding that of amorphous silicon. The key advancements are molecular-design concepts that allow multiple strain energy-dissipation mechanisms, while maintaining efficient charge-transport pathways over multiple length scales. In this perspective article, we review recent approaches to confer stretchability to polymer semiconductors while maintaining high charge carrier mobilities, with emphasis on the control of both polymer-chain dynamics and thin-film morphology. Additionally, we present molecular design considerations toward intrinsically elastic semiconductors that are needed for reliable device operation under reversible and repeated deformation. A general approach involving inducing polymer semiconductor nanoconfinement allows for incorporation of several other desired functionalities, such as biodegradability, self-healing, and photopatternability, while enhancing the charge transport. Lastly, we point out future directions, including advancing the fundamental understanding of morphology evolution and its correlation with the change of charge transport under strain, and needs for strain-resilient polymer semiconductors with high mobility retention.