Stretchable microelectromechanical systems (MEMS) possess higher mechanical deformability and adaptability than devices based on conventional solid and flexible substrates, hence they are particularly desirable for biomedical, optoelectronic, textile and other innovative applications. The stretchability performance can be evaluated by the failure strain of the embedded routing and the strain applied to the elastomeric substrate. The routings are divided into five forms according to their geometry: straight; wavy; wrinkly; island-bridge; and conductive-elastomeric. These designs are reviewed and their resistance-to-failure performance is investigated. The failure modeling, numerical analysis, and fabrication of routings are presented. The current review concludes with the essential factors of the stretchable electrical routing for achieving high performance, including routing angle, width and thickness. The future challenges of device integration and reliability assessment of the stretchable routings are addressed.