Dielectric resonators have been foreseen as a pathway for the realization of highly efficient nanoantennas and metamaterials at optical frequencies. In this paper, we study the resonant behavior of dielectric nanocylinders located on a metal plane, which in combination create dielectric resonator antennas operating in reflection mode. By implementing appropriate resonator models, the field distributions, the scaling behavior, and the efficiency of dielectric resonator antennas are studied across the spectrum from the microwave toward visible frequency bands. Numerical results confirm that a radiation efficiency above 80% can be retained up to the near-infrared with metal-backed dielectric resonators. This paper establishes fundamental knowledge toward development of high efficiency dielectric resonator antennas and reflection metasurfaces at optical frequencies. These dielectric resonators can be incorporated as basic elements in emerging applications, e.g., flat optical components, quantum dot emitters, and subwavelength sensors.