Soft electronic materials are key elements for realizing wearable, attachable, and stick-on electronics. The development of deformable and stretchable electrodes is a key research area as they are one of the most important components for soft electronic devices. Recently, significant progress in the development of deformable and stretchable electrodes has been achieved with organic materials offering electrical tunability, simple mechanical implementation, and desirable chemical and optical properties. In this review, we present recent progress in the design of stretchable electronics based on deformable conducting materials, including their fabrication and conductivity properties and the methods that are employed to enhance performance. In addition, we review the development status of organic- and carbon- based conductive materials and their hybrid composites being used for electronic applications, including carbon nanotubes, graphene, metal composites, conductive polymers, hybrid composites, and ion gel composites. The structural aspects, such as wavy or mesh configurations, of stretchable electrodes and other high-performance conducting materials are investigated intensively. Many stretchable electrodes show great potential for use in future electronics such as electronic skin (e-skin) and stretchable displays, which require reversible deformation and a high degree of operational stability.