Energy storage occurs in a variety of physical and chemical processes. In particular, defects in materials can be regarded as energy storage units since they are long-lived and require energy to be formed. Here, we investigate energy storage in non-equilibrium populations of materials defects, such as those generated by bombardment or irradiation. We first estimate upper limits and trends for energy storage using defects. First-principles calculations are then employed to compute the stored energy in the most promising elemental materials, including tungsten, silicon, graphite, diamond and graphene, for point defects such as vacancies, interstitials and Frenkel pairs. We find that defect concentrations achievable experimentally (~0.1-1 at.%) can store large energies per volume and weight, up to ~5 MJ/L and 1.5 MJ/kg for covalent materials. Engineering challenges and proof-of-concept devices for storing and releasing energy with defects are discussed. Our work demonstrates the potential of storing energy using defects in materials.