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Traditional optical lenses and the corresponding imaging systems, which are based on the optical paths when light propagates inside the bulky media, usually suffer from the bulky size, Abbe-Rayleigh diffraction restricted resolution, and limited responses to different kinds of incident light. Recently, the burgeoning development of metasurfaces comprised of artificial micro- or nano-structures at the subwavelength scale has drawn more and more attentions of the scientific community due to the intriguing abilities such as efficient light–matter interactions and multi-dimensional manipulation of optical waves, which provide profound potentials to realize functional metalens with an ultrahigh numerical aperture (NA) and with super-resolution focal spots on a compact size. Here, the research motivations, the broad outline and the recent advances of planar diffractive metalens are summarized, including the principles of metalens design, the basic components of metalens, and the development of metalens systems. Various approaches to remove the focusing aberrations are presented, which is the essential condition to realize metalens objectives and microscopy. Different types of novel metalenses are revealed, such as label-free sub-resolution metalens, nonlinear metalens, artificial intelligence-aided metalens, multifunctional metalens and reconfigurable metalens. Challenges and future goals are also presented at the end the review.