Super-oscillatory lens (SOL) and super-critical lens (SCL) are the typical representatives of planar metalens which could achieve sub-diffractive focusing and imaging in far field by means of light field modulation. Through precisely modulating the interference effect of each diffractive unit, the electromagnetic wave could be oscillated faster than its maximum frequency components in a certain region of the target plane, and then the focal spot size is controllable in lateral and longitudinal directions. Compared with the traditional optical lens, the planar metalens is much more attractive in the fields of diffractive optics and nanophotonics due to its distinct advantages of powerful focusing capabilities, compact configuration, higher design freedom and the integratable properties, etc. In this review, we briefly introduce the field modulation mechanism and design principle of planar metalens. The research advances of the super-oscillatory lens and super-critical lens, as well as their applica-tions in far-field label-free super-resolution imaging, are discussed in detail. In addition, a perspective about the future outlook of planar metalens is summarized. Since the planar metalens has powerful capability in manipu-lating the light field, the rapid development in various applications would be gradually realized in the near future.