This review is dedicated to versatile silicone rubber composites based on carbon nanotube/graphene (CNT/G) hybrid fillers. Due to their unique mechanical, electrical, thermal, and biological properties, such composites have enormous potential for medical, environmental, and electronics applications. In the scope of this paper, we have explored CNT/graphene/silicone composites with a different morphology, analyzed the synergistic effect of hybrid fillers on various properties of silicone composites, and observed the existing approaches for the fabrication of hybrid composites with a seamless, assembled, and/or foamed structure. In conclusion, current challenges and future prospects for silicone composites based on CNTs and graphene have been thoroughly discussed.