As one of the most important energy storage devices, dielectric capacitors have attracted increasing attention because of their ultrahigh power density, which allows them to play a critical role in many high-power electrical systems. To date, four typical dielectric materials have been widely studied, including ferroelectrics, relaxor ferroelectrics, anti-ferroelectrics, and linear dielectrics. Among these materials, linear dielectric polymers are attractive due to their significant advantages in breakdown strength and efficiency. However, the practical application of linear dielectrics is usually severely hindered by their low energy density, which is caused by their relatively low dielectric constant. This review summarizes some typical studies on linear dielectric polymers and their nanocomposites, including linear dielectric polymer blends, ferroelectric/linear dielectric polymer blends, and linear polymer nanocomposites with various nanofillers. Moreover, through a detailed analysis of this research, we summarize several existing challenges and future perspectives in the research area of linear dielectric polymers, which may propel the development of linear dielectric polymers and realize their practical application.