Along with the growing of population and social and technological improvements, the use of energy and natural resources has risen over the past few decades. The sustainability of using coal, oil, and natural gas as the main energy sources faces, however, substantial obstacles. Fuel cells, batteries, and super-capacitors have the highest energy densities, but due to their high-power density and rapid charge-discharge speed, regular dielectric capacitors are becoming more popular for pulsed power applications. High electric breakdown strength and high maximum but low-remnant (zero in the case of linear dielectrics) polarization are necessary for high energy density in dielectric capacitors. The high performance, multi-functionality, and high integration of electronic devices are made possible in large part by the multilayer ceramic capacitors (MLCCs). Due to their low cost, compact size, wide capacitance range, low ESL and ESR, and excellent frequency response, MLCCs play a significant role in contemporary electronic devices. From the standpoint of the underlying theories of energy storage in dielectrics, this paper emphasizes the significant problems and recent advancements in building extremely volumetric-efficient MLCCs. Following a thorough examination of the state-of-the-art, important parameters that may be used to improve energy-storage qualities are highlighted, such as controlling local structure, phase assembly, dielectric layer thickness, microstructure, conductivity, different failure modes, and the specific performance during the failure mechanism. The summary of some conclusions on the impending need for innovative materials and diagnostic methods in high-power/energy density capacitor applications appears at the end of the paper.