We review the current state-of-the-art graphene-enhanced thermal interface materials for the management of heat in the next generation of electronics. Increased integration densities, speed and power of electronic and optoelectronic devices require thermal interface materials with substantially higher thermal conductivity, improved reliability, and lower cost. Graphene has emerged as a promising filler material that can meet the demands of future high-speed and high-powered electronics. This review describes the use of graphene as a filler in curing and non-curing polymer matrices. Special attention is given to strategies for achieving the thermal percolation threshold with its corresponding characteristic increase in the overall thermal conductivity. Many applications require high thermal conductivity of composites, while simultaneously preserving electrical insulation. A hybrid filler approach, using graphene and boron nitride, is presented as a possible technology providing for the independent control of electrical and thermal conduction. The reliability and lifespan performance of thermal interface materials is an important consideration towards the determination of appropriate practical applications. The present review addresses these issues in detail, demonstrating the promise of graphene-enhanced thermal interface materials compared to alternative technologies.