Nanodielectrics, which are concentrated in polymer matrix incorporating nanofillers, have received considerable attention due to their potential benefits as dielectrics. In this paper, short-term breakdown and long-term failure properties of nanodielectrics have been reviewed. The characteristics of polymer matrix, types of nanoparticle and its content, and waveforms of the applied voltage are fully evaluated. In order to effectively comment on the published experimental data, a ratio k has been proposed to compare the electric properties of the nanodielectrics with the matrix and assess the effect for nanoparticles doping. There is evidence that the short-term breakdown properties of nanodielectrics show a strong dependence on the applied voltage waveforms. The polarity and the cohesive energy density (CED) of polymer matrix have a dramatic influence on the properties of nanodielectrics. Nanoparticle doped composites show a positive effect on the long-term failure properties, such as ageing resistance and partial discharge (PD) properties of nanocomposites are superior than microcomposites and the matrix. The larger the dielectric constant and CED of the matrix become, the more significant improvements in long-term performance appear. Based on the reported experimental results, we also present our understandings and propose some suggestions for further work.