Thin polypropylene films have played a strategic role in recent years because they are the dielectric of choice for high-energy-density and high-power-density DC-link capacitors, and have been extensively used in renewable energy and electric mobility applications. Currently, these capacitors operate at temperatures of up to 105 °C with electric fields of up to 200 V/µm, allowing high efficiency due to their low dissipation figures compared to other capacitor technologies. The rapid evolution of green energy applications demands higher energy and power density, with expected operating temperatures and electric fields of up to 115 °C and above 250 V/µm, respectively. Under such conditions, the insulation resistance of the capacitor becomes a key factor, as it may start to contribute to the dissipation of energy. A correct understanding of conduction phenomena within the dielectric is necessary for the design of new high-performance capacitors based on polypropylene film with reduced conduction losses. The scope of this review is to present and evaluate the theoretical and experimental works on thin biaxially oriented polypropylene (BOPP) films for capacitor applications with a focus on electrical conductivity at high electric field and temperature.