Significance: Research in soft robotics and wearable technologies has led to increasing demand for shape-changing materials that can be powered with portable electronics. Liquid crystal elastomers (LCEs) are a promising functional material for these applications but lack the electrical and thermal conductivity required for electrically stimulated shape-memory activation. To address this, LCEs are typically embedded with rigid fillers that enhance conductivity. However, these particles degrade the mechanical properties and shape-morphing capabilities of the LCE matrix. Here, we overcome these limitations with an advanced material architecture in which rigid filler is replaced with deformable liquid metal inclusions. This results in LCE composites that exhibit a combination of high electrical conductivity, high thermal conductivity, and actuation capabilities unlike any other soft composite.