In his seminal work on twin splitting (with S. Mueller), Bob Kohn taught us how the presence of an interfacial energy selects certain types of microstructures, i. e. removes the high degree of degeneracy of an unrelaxed non-convex ariational problem. Later, he realized that the same analysis applies to domain branching in ferromagnets (with R. Choksi) and to flux tube branching in superconductors (with S. Conti). The use of suitable interpolation inequalities freed the analysis and motivated the connection to the physically unrelated subject of coarsening in spinodal decomposition. In recent work (with H. Knuepfer), Bob Kohn showed how the above insights into twin branching allow to understand even hierarchical microstructures like Martensitic inclusions in Austenite.