Numerous applications in neuroscience research and neural prosthetics, such as retinal prostheses, spinal-cord surface stimulation for prosthetics, electrocorticogram (ECoG) recording for epilepsy detection, etc., involve electrical interaction with soft excitable tissues using a surface stimulation and/or recording approach. These applications require an interface that is able to set up electrical communications with a high throughput between electronics and the excitable tissue and that can dynamically conform to the shape of the soft tissue. Being a compliant and biocompatible material with mechanical impedance close to that of soft tissues, polydimethylsiloxane (PDMS) offers excellent potential as the substrate material for such neural interfaces. However, fabrication of electrical functionalities on PDMS has long been very challenging. This thesis work has successfully overcome many challenges associated with PDMS-based microfabrication and achieved an integrated technology platform for PDMS-based stretchable microelectrode arrays (sMEAs). This platform features a set of technological advances: (1) we have fabricated uniform current density profile microelectrodes as small as 10 microns in diameter; (2) we have patterned high-resolution (feature as small as 10 microns), high-density (pitch as small as 20 microns) thin-film gold interconnects on PDMS substrate; (3) we have developed a multilayer wiring interconnect technology within the PDMS substrate to further boost the achievable integration density of such sMEA; and (4) we have invented a bonding technology---via-bonding---to facilitate high-resolution, high-density integration of the sMEA with integrated circuits (ICs) to form a compact implant. Taken together, this platform provides a high-resolution, high-density integrated system solution for neural and muscular surface interfacing. sMEAs of example designs are evaluated through in vitro and in vivo experimentations on their biocompatibility, surface conformability, and surface recording/stimulation capabilities, with a focus on epimysial (i.e. on the surface of muscle) applications. Finally, as an example medical application, we investigate a prosthesis for unilateral vocal cord paralysis (UVCP) based on simultaneous multichannel epimysial recording and stimulation.