Metasurfaces are a topic of significant research and are used in various applications due to their unique ability to manipulate electromagnetic waves in microwave and optical frequencies. These artificial sheet materials, which are usually composed of metallic patches or dielectric etchings in planar or multi-layer configurations with subwavelength thickness, have the advantages of light weight, ease of fabrication, and ability to control wave propagation both on the surface and in the surrounding free space. Recent progress in the field has been classified by application and reviewed in this article. Starting with the development of frequency-selective surfaces and metamaterials, the unique capabilities of different kinds of metasurfaces have been highlighted. Surface impedance can be varied and manipulated by patterning the metasurface unit cells, which has broad applications in surface wave absorbers and surface waveguides. They also enable beam shaping in both transmission and reflection. Another important application is to radiate in a leaky wave mode as an antenna. Other applications of metasurfaces include cloaking, polarizers, and modulators. The controllable surface refractive index provided by metasurfaces can also be applied to lenses. When active and non-linear components are added to traditional metasurfaces, exceptional tunability and switching ability are enabled. Finally, metasurfaces allow applications in new forms of imaging.