Abstract: The Hodge conjecture has its origins in the work of Lefschetz regarding which 2 dimensional homology classes on an algebraic surface could be represented via algebraic curves on the surface. Lefschetz's solution involved the study of a class of "Poincare normal functions" on the Riemann sphere minus a finite number of points. In this talk, I will outline Lefschetz's proof and discuss some recent work of Griffiths and Green towards studying the Hodge conjecture for higher codimension cycles using normal functions on higher dimensional parameter spaces.