 Wolf construction is a mathematical model used to predict the equilibrium shape of nanoparticles based on their surface energy. It has been applied to a variety of materials including metals, alloys, semiconductors, and ceramics. Recent advances have included the use of wolf construction to study the shapes of nanoparticles with active sites, ligands, and complex metal hydrides. This article was authored by Georgios de Barmparis, Zbigniew Lodziana, Muriel Lopez, and others.