The projected increase in world energy consumption within the next 50 years, coupled with low emission requirements, has inspired an enormous effort towards the development of efficient, clean, and renewable energy sources. Efficient electrical energy storage solutions are keys to effective implementation of the electricity generated from these renewable sources. In step with the development of energy storage technology and the power electronics industry, dielectric materials with high energy density are in high demand. The dielectrics with a medium dielectric constant, high breakdown strength, and low polarization hysteresis are the most promising candidates for high-power energy storage applications. Inspiring energy densities have been achieved in current dielectrics, but challenges exist for practical applications, where the underlying mechanisms need to be understood for further enhancing their properties to meet future energy requirements. In this review, we summarize the principles of dielectric energy-storage applications, and recent developments on different types of dielectrics, namely linear dielectrics, paraelectrics, ferroelectrics, and antiferroelectrics, are surveyed, focusing on perovskite lead-free dielectrics. The new achievements of polymer-ceramic composites in energy-storage applications are also reviewed. The pros and cons of each type of dielectric, the existing challenges, and future perspectives are presented and discussed with respect to specific applications.