Building on work of Stasheff, S.A. Merkulov has shown that the harmonic forms on a compact Kahler manifold M carry a natural A-infinity multiplication. (He shows that in fact there are at least two, and that if M happens to be Calabi-Yau then there is yet a third.) We will review the definitions, construction, and a sketch of the proof. Merkulov's work raises the question of when A-infinity structures arise naturally out of associative ones in more general contexts.