Polymer-based dielectric capacitors are widely-used energy storage devices. However, although the functions of dielectrics in applications like high-voltage direct current transmission projects, distributed energy systems, high-power pulse systems and new energy electric vehicles are similar, their requirements can be quite different. Low electric loss is a critical prerequisite for capacitors for electric grids, while high-temperature stability is an essential pre-requirement for those in electric vehicles. This paper reviews recent advances in this area, and categorizes dielectrics in terms of their foremost properties related to their target applications. Requirements for polymer-based dielectrics in various power electronic equipment are emphasized, including high energy storage density, low dissipation, high working temperature and fast-response time. This paper considers innovations including chemical structure modification, composite fabrication and structure re-design, and the enhancements to material performances achieved. The advantages and limitations of these methods are also discussed.