The unique characteristics of Dielectric Resonator Antennas (DRAs) make them suitable for various niche applications throughout the spectrum, from microwave frequencies to the optical regime. One of the striking features of DRAs is their high efficiency when the resonator is realized in low-loss high-permittivity dielectric material. This interesting property arises from their radiation mechanism being mostly based on displacement currents, and opens the door to efficient device realizations towards higher frequencies where conductor losses degrade the performance of metallic resonators. This paper will highlight some of the distinctive properties of the DRAs and review their potential applications in various frequency regimes. It will in particular consider the latest developments at THz and optical frequencies, with high-efficiency realizations of reflect-arrays and magnetic mirrors.