Linear embedding via Green’s operators (LEGO) is a domain decomposition method specifically devised for the efficient solution of electromagnetic (EM) scattering and propagation problems that involve either "large" or "complex" structures or possibly both. LEGO is based on the conceptual separation of the local (near-field) interaction from the mutual (distant) ones between parts of a structure. Said separation is obtained by dividing the structure in pieces (dubbed "bricks") which are described by means of scattering operators of equivalent surface currents. The multiple scattering occurring between the bricks is accounted for by transfer operators of equivalent surface currents. Thanks to this approach, intrinsically different EM problems can be formulated in terms of integral equations which invariably take the same form. The numerical solution is then carried out by combining the baseline Method of Moments and sub-domain div-conforming basis functions with two types of macro basis functions: (1) eigencurrents and (2) Arnoldi basis functions. The features of these macro basis functions are discussed in details with the aid of selected numerical examples.