This chapter describes the nomenclature of mononuclear and polynuclear acyclic parent hydrides, monocyclic hydrocarbons and heterocycles, polycyclic parent hydrides (the extended von Baeyer system), and spiro ring systems. A new nomenclature system called phane nomenclature, a nomenclature specific to cyclic or acyclic compounds composed of rings or ring systems directly linked to each other or linked by atoms or chains; it was mainly designed to simplify the nomenclature for multiring assemblies. Fullerenes are compounds composed solely of an even number of carbon atoms, which form a cage-like fused-ring polycyclic system with twelve five-membered rings and the rest six-membered rings. Nomenclature for two common simple fullerenes, (C60-Ih)[5,6]fullerene and (C70-D5h(6))[5,6]fullerene and many of their dervatives is illustrated.