Dielectric capacitors with the prominent features of ultrafast charging–discharging rates and ultrahigh power densities are ubiquitous components in modern electronics. To meet the growing demand for electronics miniaturization, dielectric capacitors with high energy storage properties are extensively researched. The tutorial will present an overview of the recent progress in the field of nanostructured dielectric materials targeted for capacitive energy storage applications. This tutorial commences with a brief introduction of the fundamentals of dielectric materials, including primary parameters, a library of dielectric polymers, polymer nanocomposites, and bulk ceramics, and multiscale structures. Both commercial products and the latest research results are covered. While general design considerations are briefly discussed, emphasis is placed on material specifications oriented toward the dielectric energy storage applications, such as dielectric properties, temperature stability, energy density, and charge-discharge efficiency. Emphases are placed on the relationship between multiscale structures and energy storage properties and the rational structure design principles in dielectric materials. The advantages and shortcomings of the existing dielectric materials are identified. Challenges along with future research opportunities are highlighted at the end of this tutorial.