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The growing needs for human healthcare have driven the development of wearable devices for monitoring the health status of an individual. Polymers represent a promising platform for such devices due to their ability to form an intimate contact between soft organs and rigid electronic components. Stencil lithography (SL), which uses patterned membranes as a mask to locally deposit materials on substrates, provides a simple but versatile fabrication platform for realizing wearables. However, no studies have explored the deposition of materials on polymer substrates through this technique, impeding further development. Additionally, the freestanding membranes in stencils limit the geometrical design flexibility of apertures. This thesis aims to overcome such limitations, extend the use of SL for structuring stretchable liquid metal (LM) and finally demonstrate the connection of LM to silicon nanomembrane (Si NM) for stretchable Si conductors. This thesis starts by providing a systematic study on the deposition of metals on various polymers including biocompatible and biodegradable materials using SL. The metallic patterns are successfully fabricated on the polymer substrate used by SL. The geometrical and electrical characterizations are performed and discussed. Next, we propose a concept of introducing bridges on stencil membranes to extend the geometrical design flexibility of SL. The applied bridges stabilize the suspended membrane to enable arbitrary apertures. Continuous material traces are produced by taking advantage of the blurring effect. When the stencil is lifted to an appropriate distance above the substrate, the line-of-sight evaporation process results in the material deposition under the shadowed bridge region. The proposed bridge stencils allow the realization of spiral and meandering structures at the micrometer and sub-micrometer scales. The deposition on a variety of substrate materials reveals the versatility of the proposed bridge stencil. We further extend the use of SL for the realization of stretchable LM electronics. A hybrid process combining SL and centrifugal force-assisted patterning of LM is presented. The selective wetting behaviour of oxide-removed eutectic gallium-indium (EGaIn) on metal patterns defined by SL enables micrometer LM patterns on elastomeric substrates. Microscale LM patterns are achieved by efficiently removing the excess material by the centrifugal forces experienced from spinning the substrate. The geometrical and electrical properties of LM patterns on stretchable substrates are characterized. Utilizing bridge stencils, EGaIn serpentine conductors and interdigitated capacitors are fabricated and characterized. Lastly, we translate the LM patterning technique to realize stretchable Si NM conductors using LM as interconnections. Si NM provides exceptional mechanical flexibility and electrical properties, an excellent candidate for wearable electronic applications. The use of LM significantly reduces the need for complex wiring while providing excellent stretchability. PI films are added underneath Si NMs to allow the device to sustain large mechanical deformation. The simulations detail the design strategy of the proposed device configuration. The fabrication methods, including the transfer of single-crystalline Si NMs to polymers and the integration of LM to Si NMs, are developed. The electrical characterizations under mechanical deformation are performed and the results are discussed.