Compare with conventional refractive-type optical lens, planar diffraction lens has shown significant advantages in terms of reduced volume,light weight, facile fabrication, and easy to integration, etc. The traditional planar diffractive lens, for instance Fresnel zone plate, usually focuses light into an Airy spot with the lateral size of 0.61λ/NA, which is known as Rayleigh Criterion. Squeezing the focal spot beyond Rayleigh criterion will bring more benefits for practical applications. Different from the refractive type optical lens, planar diffraction lens provides a higher degree of freedom for the light field modulation, the lateral size of the focal spot can be customized by optimizing the structural parameters. Optical super-oscillation refers to the phenomenon in which a band limited function can be oscillated much faster than the fastest Fourier components in the focal region through delicately control the interference effect, then a sub-diffraction limited focal spot will be obtained in the focal plane. Under the guidance of the optical super-oscillation theory, planar diffractive lenses with sub-diffraction limited light modulation property in free space attract extensive attention in recent year. As its typical representatives, supercritical lens becomes one of the hot topics in the research field of planar metalenses, owing to its capability of effective balancing the lateral size and focusing efficiency of the sub-diffraction limited focal spot. To date, several different kinds of configurations are usually used to construct the supercritical lens, including photo sieves, metasurfaces, etc. Nevertheless, the zone plates type with concentric phase or amplitude belts is still the favorite configuration for the construction of supercritical lens. The super-oscillation condition in the focal plane could be accomplished through the optimization of the width and radial position of each zone belt. To acquire the insightful meaning in physical level about the constructive and destructive interference process, optimization-free algorithm is another effective technique for the designing of the supercritical lens. By utilizing the optimization-free technique, a customized focusing field with significantly large field of view can be achieved. Supercritical lens with binary amplitude and binary phase schemes is the easiest way to be implemented. However, the focusing efficiency is relatively small for such binary configuration. Discretizing the binary phase into multilevel phase configuration could be significantly improve the focusing efficiency. By using the sub-diffraction limit focal spot, several attractive applications have been demonstrated, including label-free far-field optical super-resolution imaging and high-density light induced magnetic holography, etc. In this review, we summarized the research advances of the supercritical lens, including the design principle, light modulation schemes, and its practical applications. Finally, a conclusion and short perspective are presented from an application-friendly point of view. The supercritical lens provides an effective method to break the diffraction limit. Its super-resolution focusing and imaging property is purely physical without any material response process. At the same time, its micron-level structure feature size enables the lens to be fabricated by the mature, fast and low-cost technology, which provides feasibility for its massive production. It has a wide application prospect in microscopic imaging, telescopic system, failure detection, precision machining, high density storage and other fields.