High-k polymer nanocomposites have received increased research interest by virtue of integrating high dielectric constant nanofiller with high breakdown strength, flexibility, and ease of processing of a matrix. With outstanding anisotropy, high-aspect-ratio nanofillers have proved to be much more efficient enhancers of the dielectric properties of nanocomposites when compared with traditional zero-dimensional (0D) fillers, leading to many dielectric and energy storage applications. This review summarizes the latest research on one-dimensional (1D) and quasi-1D fillers based high-k polymer nanocomposites with the focus on the superiority of 1D or quasi-1D high-k fillers in enhancing the dielectric properties and energy storage capability of polymer nanocomposites. Dielectric anisotropy, which plays a critical role in determining the dielectric properties and energy storage capability of polymer nanocomposites, was highlighted and the experimental methodologies for achieving anisotropic dielectric polymer nanocomposites were reviewed. The fundamental electrical parameters, such as dielectric constant, dielectric non linearity, dielectric loss and electrical conduction, and breakdown strength of dielectric polymer composites, are also discussed. Given the recent progress, guidelines for the future development of high-k polymer nanocomposites with dielectric and energy storage applications were proposed.