The development of intrinsically stretchable electronics poses great challenges in synthesizing elastomeric conductors, semiconductors and dielectric materials. While a wide range of approaches, from special macrostructural engineering to molecular synthesis, have been employed to afford stretchable devices, this review surveys recent advancements in employing various morphological and nanostructural control methods to impart mechanical flexibility and/or to enhance electrical properties. The focus will be on (1) embedding percolation networks of one-dimensional conductive materials such as metallic nanowires and carbon nanotubes in an elastomer matrix to accommodate large external deformation without imposing a large strain along the one-dimensional materials, (2) design strategies to achieve intrinsically stretchable semiconductor materials that include direct blending of semiconductors with elastomers and synthesizing semiconductor polymers with appropriate side chains, backbones, cross-linking networks, and flexible blocks, and (3) employing interpenetrating polymer networks, bottlebrush structures and introducing inclusions in stretchable polymeric dielectric materials to improve electrical performance. Moreover, intrinsically stretchable electronic devices based on these materials, such as stretchable sensors, heaters, artificial muscles, optoelectronic devices, transistors and soft humanoid robots, will also be described. Limitations of these approaches and measures to overcome them will also be discussed. The development of intrinsically stretchable electronics poses great challenges in synthesizing elastomeric conductors, semiconductors and dielectric materials.