As two-dimensional metamaterials, metasurfaces have received rapidly increasing attention from researchers all over the world. Unlike three-dimensional metamaterials, metasurfaces can be utilized to control the electromagnetic waves within one infinitely thin layer, permitting substantial advantages, such as easy fabrication, low cost, and high degree of integration. This paper reviews the history and recent development of metasurfaces, with particular emphasis on the theory and applications relating to the frequency response, phase shift, and polarization state control. Based on the current status of various applications, the challenges and future trends of metasurfaces are discussed.