Nanophotonics allows the manipulation of light on the subwavelength scale. Optical nanoantennas are nanoscale elements that enable increased resolution in bioimaging, novel photon sources, solar cells with higher absorption, and the detection of fluorescence from a single molecule. While plasmonic nanoantennas have been extensively explored in the literature, dielectric nanoantennas have several advantages over their plasmonic counterparts, including low dissipative losses and near-field enhancement of both electric and magnetic fields. Nanoantennas increase the optical density of states, which increase the rate of spontaneous emission due to the Purcell effect. The increase is quantified by the Purcell factor, which depends on the mode volume and the quality factor. It is one of the main performance parameters for nanoantennas. One particularly interesting feature of dielectric nanoantennas is the possibility of integrating them into optical resonators with a high quality-factor, further improving the performance of the nanoantennas and giving very high Purcell factors. This review introduces the properties and parameters of dielectric optical nanoantennas, and gives a classification of the nanoantennas based on the number and shape of the nanoantenna elements. An overview of recent progress in the field is provided, and a simulation is included as an example. The simulated nanoantenna, a dimer consisting of two silicon nanospheres separated by a gap, is shown to have a very small mode volume, but a low quality-factor. Some recent works on photonic crystal resonators are reviewed, including one that includes a nanoantenna in the bowtie unit-cell. This results in an enormous increase in the calculated Purcell factor, from 200 for the example dimer, to 8 × 106 for the photonic crystal resonator. Some applications of dielectric nanoantennas are described. With current progress in the field, it is expected that the number of applications will grow and that nanoantennas will be incorporated into new commercial products. A list of relevant materials with high refractive indexes and low losses is presented and discussed. Finally, prospects and major challenges for dielectric nanoantennas are addressed.