Triboelectric and piezoelectric nanogenerators are two recently developed technologies for effective harvesting of ambient mechanical energy for the creation of self-powered systems. The advantages of triboelectric and piezoelectric nanogenerators such as large open-circuit output voltage, low cost, ease-of-fabrication, and high conversion efficiency enable their application as new flexible sensors, wearable devices, soft robotics and machines. This perspective provides an overview of the current state of the art in triboelectric and piezoelectric devices that are used as self-powered sensors and energy harvesters for soft robots and machines; hybrid approaches that combine the advantages of both mechanisms are also discussed. To improve system performance and efficiency, the potential of providing self-powered soft systems with a degree of multi-functionality is investigated. This includes optical-sensing, transparency, self-healing, water-resistance, photoluminescence or an ability to operate in hostile environments such as low temperature, high humidity or high strain/stretch. Finally, areas for future research directions are identified.