Structures and methods for cloaking an object to electromagnetic radiation at the microwave and terahertz frequencies include disposing a plurality of graphene sheets about the object. Intermediate layers of a transparent dielectric material can be disposed between graphene sheets to optimize the performance. In other embodiments, the graphene can be formulated into a paint formulation or a fabric and applied to the object. The structures and methods absorb at least a portion of the electromagnetic radiation at the microwave and terabyte frequencies.