The resolution of conventional optical elements and systems has long been perceived to satisfy the classic Rayleigh criterion. Paramount efforts have been made to develop different types of superresolution techniques to achieve optical resolution down to several nanometres, such as by using evanescent waves, fluorescence labelling, and postprocessing. Superresolution imaging techniques, which are noncontact, far field and label free, are highly desirable but challenging to implement. The concept of superoscillation offers an alternative route to optical superresolution and enables the engineering of focal spots and point-spread functions of arbitrarily small size without theoretical limitations. This paper reviews recent developments in optical superoscillation technologies, design approaches, methods of characterizing superoscillatory optical fields, and applications in noncontact, far-field and label-free superresolution microscopy. This work may promote the wider adoption and application of optical superresolution across different wave types and application domains.