The state-of-the art in the design and the manufacture methods of the different electromagnetic shielding materials has been reviewed. This topic has become a mainstream field of research because of the electromagnetic pollution generated by telecommunication technology development. The review is centred in absorbent materials and shows a general overview of how the absorption properties of such composites can be tailored through changes in geometry, composition, morphology, and the filler particles content. Although different types of materials are explained, the text is mainly focused on carbon materials such as graphene and carbon nanotubes. In this way, the importance of the dispersion of the conductive fillers in different polymer matrices is discussed. In addition, an extensive study on new complex architectures such as foam-based materials is presented. Finally, the combination of carbon fillers with other constituents such as metallic nanoparticles is mentioned. In all these studies, the efficiency of the composites as absorbent or reflective of electromagnetic radiation is discussed.