Metalenses are new advanced planar optical devices based on the metamaterials. They can control the amplitude, phase, and polarization of incident lights with high free degrees to satisfy application requirements. Furthermore, they can perform various functions through different structural designs, such as diffraction-limited focusing and aberration correction. In this paper, we summarize the basic principles, applications, and progress of metalenses. Based on the excitation principle, we classify metalenses into plasmonic and dielectric metalenses. Based on the function, we classify them into tunable, aberration cancellation, and broadband achromatic metalenses. We also summarize the parameter data, advantages and disadvantages, and commercialization process of relevant research. Moreover, we discuss the problems and challenges faced by metalenses and recommend future research directions. The main purpose of this paper is to clarify metalenses and provide potential inspiration for designing high-performance metalenses.