An electronic device may be provided with a phased antenna array and a display cover layer. The phased antenna array may include a dielectric resonator antenna. The dielectric resonator antenna may include a dielectric resonating element embedded in a lower permittivity dielectric substrate. The substrate and the resonating element may be mounted to a flexible printed circuit. A slot may be formed in ground traces on the flexible printed circuit and aligned with the resonating element. The slot may excite resonant modes of the resonating element. The resonating element may convey corresponding radio-frequency signals through the cover layer. A dielectric matching layer may be interposed between the resonating element and the cover layer. If desired, the slot may radiate additional radio-frequency signals and the matching layer may have a tapered shape. Dielectric resonator antennas for covering different polarizations and frequencies may be interleaved across the array.