With reference to inverse scattering from an unknown object of limited extension embedded in a homogeneous background at a fixed frequency, we show that only a finite-dimensional representation of the unknown contrast can be hopefully retrieved. Exploiting the quasi-band-limitedness property of scattered fields, an accurate upper bound to the dimension of such a space is evaluated in both the single incidence and multiview cases. Moreover, effective schemes are given to collect all the information available from the scattering experiments in a nonredundant manner. As a by-product, an optimal (minimally redundant) sampling strategy for the monostatic radar cross section is also provided. Finally, we briefly discuss how the requirement for a globally effective and reliable solution scheme can lead to a reduction of the actually retrievable information.