Nowadays, there are growing demands for developing economical and multi-functional polymeric materials that simultaneously have high thermal conductivity, optimized electrical conductivity, and improved mechanical properties. Due to its outstanding physical and mechanical properties, graphene can significantly endow epoxy polymers with novel properties. As obtaining large-scale production of graphene is crucial for developing epoxy composites, this review firstly provides insight into the newly developed methods that can balance between quality and scalability of graphene. Then, the thermal and electrical conduction mechanisms of graphene and its polymer composites are illustrated in detail. Additionally, the recent progress of graphene to concurrently regulate the thermal, electrical, and mechanical properties of epoxies is comprehensively reviewed, highlighting the influence of graphene aspect ratio, graphene derivatives, surface modification, orientation, dispersion, and the inclusion of hybrids. This study presents the state-of-the-art review of the established graphene-based epoxy composites for electrically conductive and insulative applications to provide comprehensive guidelines for researchers seeking to attain high-performance materials.