The elemental compositions of archaeological artefacts, ancient and medieval coins, and metallic art objects have been determined by non-destructive neutron activation analysis. Examples are given of studies of prehistoric trade routes and cultural contacts based on the identification of the geologic origins of obsidian artefacts, of early economic systems based on the determination of debasement patterns in Medieval Islamic and Western gold and silver coinage, the region of manufacture as well as authentication of ancient metallic art objects based on trace element analysis. Special procedures devised for performing these analyses are described.