Stretchable hybrid electronics (SHE) that combine high-performance rigid electronic devices with stretchable interconnects offer a facile route for accessing and processing bio-signals and human interactions. Incorporated with sensors and wireless communications, SHE achieves novel applications such as biomedical diagnosis, skin prosthetics, and robotic skin. The implementation of reliable SHE requires the comprehensive development of stretchable electrodes, bonding techniques, and strain-engineered integration schemes. This review covers the recent development of enabling technologies for SHE in terms of materials, structures, and system engineering. We introduce various strategies for stretchable interconnects based on novel materials and structural designs. In particular, we classify SHE into three groups based on strain-relief configurations: thin-film devices on rigid islands, rigid devices with stretchable bridges, and flexible circuits with stretchable bridges. Appropriate methods for substrates, stretchable interconnects, and bonding between rigid and soft components and their pros and cons are extensively discussed. We also explore state-of-the-art SHE in advanced human-machine interfaces and discuss the challenges and prospects for future directions.