Metasurfaces, also known as 2D artificial metamaterials, are attracting great attention due to their unprecedented performances and functionalities that are hard to achieve by conventional diffractive or refractive elements. With their sub-wavelength optical scatterers, metasurfaces have been utilized to freely modify different characteristics of incident light such as amplitude, polarization, phase, and frequency. Compared to traditional bulky lenses, metasurface lenses possess the advantages of flatness, light weight, and compatibility with semiconductor manufacture technology. They have been widely applied to a range of scenarios including imaging, solar energy harvesting, optoelectronic detection, etc. In this review, we will first introduce the fundamental design principles for metalens, and then report recent theoretical and experimental progress with emphasis on methods to correct chromatic and monochromatic aberrations. Finally, typical applications of metalenses and corresponding design rules will be presented, followed by a brief outlook on the prospects and challenges of this field.