The rapid growth of the electronics industry and the increasing consumption of electronic devices have resulted in the generation of large amounts of non-recyclable waste and environmental pollutants. In addition, conventional inorganic materials used in electronic devices are generally brittle, expensive, and mechanically rigid, making them unsuitable for the next generation of soft, wearable, and stretchable electronics. Therefore, the development of flexible polymers and polymer-based nanocomposites has emerged as one of the most important research directions in flexible electronics. Among the various polymeric materials, polydimethylsiloxane (PDMS) has become one of the most widely used substrates for flexible and stretchable electronic devices due to its excellent flexibility, optical transparency, biocompatibility, chemical stability, and ease of processing. Furthermore, the incorporation of conductive nanomaterials such as graphene, carbon nanotubes, and metallic nanowires into PDMS matrices has enabled the fabrication of nanocomposites with high electrical conductivity, superior mechanical stability, and excellent stretchability. These hybrid structures play a significant role in the development of transparent conductive electrodes, wearable sensors, flexible displays, and other next-generation electronic devices. This review article discusses the role of polymers, particularly PDMS-based systems and conductive nanocomposites, in the development of flexible and stretchable electronics, while highlighting the major advantages, challenges, and future perspectives of these advanced materials.