Why green functions for matching?

Work on Surface Green Function Matching (SGFM) has been the subject of extensive collaborations with members of the Iberoamerican community of solid state physicists. The conceptual frame, the basic general results and their meaning, form and generality of scope are discussed. The practical aspects of SGFM calculations are discussed, with attention to formal arguments which prove useful in practice and to computational transfer matrix techniques. A wide range of selected applications are presented. The approach taken is a historical-not strictly chronological-perspective with emphasis on the significance of the results in their own time, as well as a reflection of the collaborations with many members of this community.