Stretchable electronic devices with intrinsically stretchable components have significant inherent advantages, including simple fabrication processes, a high integrity of the stacked layers, and low cost in comparison with stretchable electronic devices based on non‐stretchable components. The research in this field has focused on developing new intrinsically stretchable components for conductors, semiconductors, and insulators. New methodologies and fabrication processes have been developed to fabricate stretchable devices with intrinsically stretchable components. The latest successful examples of stretchable conductors for applications in interconnections, electrodes, and piezoresistive devices are reviewed here. Stretchable conductors can be used for electrode or sensor applications depending on the electrical properties of the stretchable conductors under mechanical strain. A detailed overview of the recent progress in stretchable semiconductors, stretchable insulators, and other novel stretchable materials is also given, along with a discussion of the associated technological innovations and challenges. Stretchable electronic devices with intrinsically stretchable components such as field‐effect transistors (FETs), photodetectors, light‐emitting diodes (LEDs), electronic skins, and energy harvesters are also described and a new strategy for development of stretchable electronic devices is discussed. Conclusions and future prospects for the development of stretchable electronic devices with intrinsically stretchable components are discussed.