This work is aimed at reviewing through a detailed analysis the performances, the features, and the limitations of the BCS-based technique when dealing with reference and representative synthesis problems concerned with (a) real excitations and symmetrical patterns as well as (b) shaped-beam sparse arrays (i.e., complex excitations and asymmetrical pattern). The abstract is organized as follows. In Sect. II, the synthesis problem at hand is mathematically formulated as an example of a more general inversion problem and recast to the BCS framework. A set of representative results is presented to assess the potentialities and the current limitations of the synthesis approach.