In this work we address the distance dependence of reconfigurable intelligent surfaces (RIS). As differentiating factor to other works in the literature, we focus on the array near-field, what allows us to comprehend and expose the promising potential of RIS. The latter mostly implies an interplay between the physical size of the RIS and the size of the Fresnel zones at the RIS location, highlighting the major role of the phase. To be specific, the point-like (or zero-dimensional) conventional scattering characterization results in the well-known dependence with the fourth power of the distance. On the contrary, the characterization of its near-field region exposes a reflective behavior following a dependence with the second and third power of distance, respectively, for a two-dimensional (planar) and one-dimensional (linear) RIS. Furthermore, a smart RIS implementing an optimized phase control can result in a power exponent of four that, paradoxically, outperforms free-space propagation when operated in its near-field vicinity. All these features have a major impact on the practical applicability of the RIS concept. As one contribution of this work, the article concludes by presenting a complete signal characterization for a wireless link in the presence of RIS on all such regions of operation.