Recent developments in various technologies, such as hybrid electric vehicles and pulsed power systems, have challenged researchers to discover affordable, compact, and super-functioning electric energy storage devices. Among the existing energy storage devices, polymer nanocomposite film capacitors are a preferred choice due to their high power density, fast charge and discharge speed, high operation voltage, and long service lifetime. In the past several years, they have been extensively researched worldwide, with 0D, 1D, and 2D nanofillers being incorporated into various polymer matrixes. However, 1D nanofillers appeared to be the most effective in producing large dipole moments, which leads to a considerably enhanced dielectric permittivity and energy density of the nanocomposite. As such, this Review focuses on recent advances in polymer matrix nanocomposites using various types of 1D nanofillers, i.e., linear, ferroelectric, paraelectric, and relaxor-ferroelectric for energy storage applications. Correspondingly, the latest developments in the nanocomposite dielectrics with highly oriented, surface-coated, and surface-decorated 1D nanofillers are presented. Special attention has been paid to identifying the underlying mechanisms of maximizing dielectric displacement, increasing dielectric breakdown strength, and enhancing the energy density. This Review also presents some suggestions for future research in low-loss, high energy storage devices.