The phenomenon of optical superoscillations first introduced in 2006 (J. Phys. A 39, 6965, 2006) and experimentally identified shortly after (Appl. Phys. Lett. 90, 091119, 2007) describes the rapid subwavelength spatial variations of intensity and phase of light in complex electromagnetic fields formed by interference of several coherent waves. Its discovery stimulated the intense revision of the limits of classical electromagnetism in particular the study of structure of superoscillatory fields in free space including unlimitedly small energy hotspots, phase singularities, energy backflow, anomalously high wavevectors and their intriguing similarities to the evanescent plasmonic fields on metals. In recent years, the better understanding of superoscillatory light has led to the development of superoscillatory lensing, imaging and metrology technologies. Dielectric, metallic and metamaterial nanostructured superoscillatory lenses have been introduced that are able to create hotspots smaller than allowed by conventional lenses. Far-field, label-free non-intrusive deeply subwavelength superresolution imaging and metrology techniques that exploit high light localization and rapid variation of phase in superoscillatory fields have been developed including new approaches based on artificial intelligence. The present paper reviews the fundamental properties of superoscillatory optical fields and examines emerging technological applications of superoscillations.