Metasurfaces (MTSs) have emerged in the last years as a promising platform for next generation planar devices in a broad range of frequencies, thanks to their unique field manipulation capability. In particular, in the microwave range this solution is characterized by low-cost, lightweight, and simple integration with electronic circuits, since MTSs can be realized in PCB technology by printing electrically small patches over a dielectric slab. The MTS behavior can then be conveniently described in terms of homogenized boundary conditions of impedance type. Spatial modulation of these boundary conditions allows one to implement a broad class of functionalities, involving space wave or surface wave control, as well as conversion from surface waves to leaky waves. This paper reviews numerical and analytical models, design procedures and microwave applications of modulated MTSs, with particular emphasis on surface wave manipulation, and it discusses expected future developments of this technology.INDEX TERMS Impedance boundary conditions, leaky wave antennas, metasurfaces, periodic structures, planar antennas, planar lenses, surface waves.This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.