We use terahertz and multi-terahertz spectroscopy to investigate optical properties of three-dimensional (3D) graphene across a wide frequency range of 0.15–10 THz. We explore the electromagnetic shielding, stealth, and absorber capabilities of 3D graphene samples annealed at various temperatures up to 1300 °C. We show that the tradeoff between the transmitted, absorbed and reflected power of the materials can be controlled by the annealing temperature through a fine broadband tuning of the refractive and absorptive indices of the material. This ultralight system (with a specific mass of ) is capable of acting as a stealth element (non-annealed sample, ), THz absorber (annealing at 750 °C, ) or a shielding coating (annealing at 1300 °C, ) within an ultrabroadband range of 0.2–7 THz. All these properties can be combined by stacking these materials on top of each other, which provides unique opportunities for THz applications.