In contrast to conventional hardware that are engineered from rigid materials, soft-matter machines and electronics are primarily composed of soft polymers, gels, and fluids. They can function as artificial skin and muscle that enable physical human-machine interaction and robots that approach the rich versatility of natural organisms. Progress in “soft-matter engineering” requires new materials and methods of integration that achieve unique combinations of electronic, robotic, and passive mechanical functionality. In this talk, I will review current paradigms in soft electronics and actuation and show how some of their existing limitations can be overcome with a novel class of soft materials embedded with liquid metal (LM). Inclusions for these LM-embedded elastomer (LMEE) systems can range from microfluidic LM networks that function as highly stretchable circuits to dispersions of LM microdroplets that exhibit unique electrical and thermal properties. I will focus special attention on the central role of solid mechanics and how existing theoretical models can be adapted to examine effective medium properties and electromechanical coupling. I will also discuss the role of conductive elastomers and liquid-phase electronics in the broader context of wearable computing and soft robotics. This will include highlights of recent work on tactile electronic skin sensing, mechanical rigidity-tuning, and thermal actuation with shape memory alloy.