This paper revises the use of polymer nanocomposites to attenuate high-energy electromagnetic radiation (HE-EMR), such as gamma radiation. As known, high-energy radiation produces drastic damage not only in facilities or electronic devices but also to life and the environment. Among the different approaches to attenuate the HE-EMR, we consider the use of compounds with a high atomic number (Z), such as lead, but as known, lead is toxic. Therefore, different works have considered low-toxicity post-transitional metal-based compounds, such as bismuth. Additionally, nanosized particles have shown higher performance to attenuate HE-EMR than those that are micro-sized. On the other hand, materials with π-conjugated systems can also play a role in spreading the energy of electrons ejected as a consequence of the interaction of HE-EMR with matter, preventing the ionization and bond scission of polymers. The different effects produced by the interactions of the matter with HE-EMR are revised. The increase of the shielding properties of lightweight, flexible, and versatile materials such as polymer-based materials can be a contribution for developing technologies to obtain more efficient materials for preventing the damage produced for the HE-EMR in different industries where it is found.