The concept of dual vector spaces was first introduced about 100 years ago by Hahn (1927), Schauder (1930), and Banach (1932). The word dual itself was first introduced by Bourbaki (1938). When the concept of a vector space over a field is broadened to a Grassmann algebra of null vectors over a field, a new concept of local duality arises. This paper explores the relationships between global and local duality in Grassmann algebras of null vectors, and the Clifford geometric algebras they become.