With the modern development of power electrification, polymer nanocomposite dielectrics (or nanodielectrics) have attracted significant research attention. The idea is to combine the high dielectric constant of inorganic nanofillers and the high breakdown strength/low loss of a polymer matrix for higher energy density polymer film capacitors. Although impressively high energy density has been achieved at the laboratory scale, there is still a large gap from the eventual goal of polymer nanodielectric capacitors. In this review, we focus on essential material issues for two types of polymer nanodielectrics, polymer/conductive nanoparticle and polymer/ceramic nanoparticle composites. Various material design parameters, including dielectric constant, dielectric loss, breakdown strength, high temperature rating, and discharged energy density will be discussed from both fundamental science and high-voltage capacitor application points of view. The objective is to identify advantages and disadvantages of the polymer nanodielectric approach against other approaches utilizing neat dielectric polymers and ceramics. Given the state-of-the-art understanding, future research directions are outlined for the continued development of polymer nanodielectrics for electric energy storage applications.