Dielectric capacitors have garnered significant attention in recent decades for their wide range of uses in contemporary electronic and electrical power systems. The integration of a high breakdown field polymer matrix with various types of fillers in dielectric polymer nanocomposites has attracted significant attention from both academic and commercial sectors. The energy storage performance is influenced by various essential factors, such as the choice of the polymer matrix, the filler type, the filler morphologies, the interfacial engineering, and the composite structure. However, their application is limited by their large amount of filler content, low energy densities, and low-temperature tolerance. Very recently, the utilization of two-dimensional (2D) materials has become prevalent across several disciplines due to their exceptional thermal, electrical, and mechanical characteristics. Compared with zero-dimensional (0D) and one-dimensional (1D) fillers, two-dimensional fillers are more effective in enhancing the dielectric and energy storage properties of polymer-based composites. The present review provides a comprehensive overview of 2D filler-based composites, encompassing a wide range of materials such as ceramics, metal oxides, carbon compounds, MXenes, clays, boron nitride, and others. In a general sense, the incorporation of 2D fillers into polymer nanocomposite dielectrics can result in a significant enhancement in the energy storage capability, even at low filler concentrations. The current challenges and future perspectives are also discussed.