Optical metasurfaces are thin‐layer subwavelength‐patterned structures that interact strongly with light. Metasurfaces have become the subject of several rapidly growing areas of research, being a logical extension of the field of metamaterials towards their practical applications. Metasurfaces demonstrate many useful properties of metadevices with engineered resonant electric and magnetic optical responses combined with low losses of thin‐layer structures. Here we introduce the basic concepts of this rapidly growing research field that stem from earlier studies of frequency‐selective surfaces in radiophysics, being enriched by the recent development of metamaterials and subwavelength nanophotonics. We review the most interesting properties of photonic metasurfaces, demonstrating their useful functionalities such as frequency selectivity, wavefront shaping, polarization control, etc. We discuss the ways to achieve tunability of metasurfaces and also demonstrate that nonlinear effects can be enhanced with the help of metasurface engineering.