The term “metasurface” (MTS) denotes an artificial surface constituted by a distribution of electrically small elements that collectively exhibit equivalent homogeneous boundary conditions (BCs) to an interacting electromagnetic field. MTSs are becoming increasingly popular due to the technological simplification that they offer with respect to volumetric metamaterials. In this article, we review the basic theory behind microwave MTSs seen as reconfigurable intelligent surfaces (RISs), oriented to the future visionary challenge of a smart radio environment. To this end, two different typologies of MTS are reviewed: surface-wave-based MTSs and nonspecular reflective MTSs. Both types can be effectively characterized using simplified problems that locally match the homogenized, modulated BCs. A different use of these problems allows for an accurate design of radiated and scattered fields. An accurate ray representation is also suggested, which allows for an effective description of the scattered field also in the Fresnel region and for the insertion of the MTS description in ray-tracing tools for network planning. Several examples of practical implementation are shown, and the challenges in applying electronic reconfigurability are discussed.