Electronic systems that offer elastic mechanical responses to high strain deformations are of growing interest, due to their ability to enable new electrical, optical and biomedical devices and other applications whose requirements are impossible to satisfy with conventional wafer-based technologies or even with those that offer simple bendability. This paper describes materials and mechanical design strategies for classes of electronic circuits that offer extremely high flexibility and stretchability over large area, enabling them to accommodate even demanding deformation modes, such as twisting and linear stretching to 'rubber-band' levels of strain over 100%. The use of printed single crystalline silicon nanomaterials for the semiconductor provides performance in flexible and stretchable complementary metal-oxide-semiconductor (CMOS) integrated circuits approaching that of conventional devices with comparable feature sizes formed on silicon wafers. Comprehensive theoretical studies of the mechanics reveal the way in which the structural designs enable these extreme mechanical properties without fracturing the intrinsically brittle active materials or even inducing significant changes in their electrical properties. The results, as demonstrated through electrical measurements of arrays of transistors, CMOS inverters, ring oscillators and differential amplifiers, suggest a valuable route to high performance stretchable electronics that can be integrated with nearly arbitrary substrates. We show examples ranging from plastic and rubber, to vinyl, leather and paper, with capability for large area coverage.