Soft systems are machines that are chiefly fabricated with soft (highly compliant) materials. These soft machines often take inspiration from biology, mimicking the softness and flexibility of organisms, like the octopus, to acclimate to unstructured environments, or mimicking the elasticity of skin to provide harmonious human-machine interface. Since soft systems improve the biocompatibility and versatility of conventional hard systems, they can make up for the shortfalls of hard systems and have great potential in plenty of applications, such as: physical assistive robotics; wearable computing; health monitoring; and human-machine interaction. Electronic components can provide crucial and fundamental functionalities, such as data acquisition (sensors), data processing (microprocessors), data transmission (antennas), and data visualisation (displays), for the systems they serve. Integrating electronics into soft systems will inevitably enrich the capabilities of these systems, enabling them to detect the surrounding environment and transmit information to the real world. Integrating electronics into soft structures introduces unique challenges which arise from materials compatibility and integration in fabrication and interfacing. The majority of integrated electronic circuits are made from rigid materials that are difficult to bend or stretch, while the production material of soft systems has given priority to flexible and stretchable materials, such as hydrogels and silicones. When solid-state electronic components are embedded in soft materials, delamination tends to occur at the interface between the soft and the hard materials when the devices deform. My Ph.D. study focuses on developing fully integrated soft electronic systems by improving the integration between electronic components and soft materials, and by creating unique flexible and stretchable electronic circuit components (using liquid metal and silicone materials). These developments enable fully integrated soft electronic systems with the functionalities of data acquisition, data processing, data transmission, and data visualisation. This thesis includes: (i) a systematic review of previous research on soft systems and stretchable soft electronics; (ii) the development of a rapid-prototyping technique for soft-lithography masters; (iii) the development of a high resolution pressuresensor soft system that can transduce normal force into a digital output; (iv) the development of a new passive wireless soft sensor, which benefits from a combination of radio-frequency identification (RFID) tag design and microfluidic sensor fabrication technologies. (v) the development of a method, which has the potential to be mass-manufacturable, to fabricate soft printed circuit boards. In summary, I describe the design and fabrication of soft electronic components with unique repeatable approaches that I developed and I provide methods to integrate electronic components into integrated soft electronic systems. My studies contribute to many cutting-edge research fields, such as soft robotics, wearable devices, microfluidics, and prosthetics.