We discuss the evolution of the theory of duality between holomorphic functions and analytic functionals. The theory originated with the work of Fantappié, but was transformed into a much more far-reaching theory through the work of Grothendieck and the development of the theory of locally convex topological vector spaces. The ideas brought forward in that context eventually led to Sato’s discovery of hyperfunctions and remain very much alive in modern work on hypercomplex analysis.