Binary mixtures of liquid metal (LM) or low-melting-point alloy (LMPA) in an elastomeric or fluidic carrier medium can exhibit unique combinations of electrical, thermal, and mechanical properties. This emerging class of soft multifunctional composites have potential applications in wearable computing, bio-inspired robotics, and shape-programmable architectures. The dispersion phase can range from dilute droplets to connected networks that support electrical conductivity. In contrast to deterministically patterned LM microfluidics, LMPA- and LM-embedded elastomer (LMEE) composites are statistically homogenous and exhibit effective bulk properties. Eutectic Ga-In (EGaIn) and Ga-In-Sn (Galinstan) alloys are typically used due to their high conductivity, low viscosity, negligible nontoxicity, and ability to wet to nonmetallic materials. Because they are liquid-phase, these alloys can alter the electrical and thermal properties of the composite while preserving the mechanics of the surrounding medium. For composites with LMPA inclusions (e.g., Field's metal, Pb-based solder), mechanical rigidity can be actively tuned with external heating or electrical activation. This progress report, reviews recent experimental and theoretical studies of this emerging class of soft material architectures and identifies current technical challenges and opportunities for further advancement.