The possibility of making a given object transparent to the impinging radiation, or cloaking it, by employing a suitable metamaterial or plasmonic cover has been recently studied theoretically, showing how this technique may overcome the limitations of other currently available techniques. Here we discuss the underlying mechanisms, physical insights and some computer simulations on the role of such homogeneous isotropic metamaterial covers near their plasma frequency in order to dramatically reduce the fields scattered by a given object. Not requiring any absorptive process, any anisotropy or inhomogeneity, and any interference cancellation, in this contribution we demonstrate, using full-wave numerical simulations, how a homogeneous isotropic plasmonic material shell may basically "re-route" the impinging field in such a way to make dielectric and even conducting or metallic objects of a certain size nearly transparent to an outside observer placed in its near as well as in its far field. In addition, it is discussed in detail how this technique, relying on a non-resonant phenomenon, is fairly robust to relatively high variations of the shape and of the geometrical and electromagnetic properties of the cloaked object.