  This note is a survey of the enumerative geometry of rational curves on
Calabi-Yau threefolds, based on a talk given by the author at the May 1991
Workshop on Mirror Symmetry at MSRI. An earlier version appeared in "Essays on
Mirror Manifolds"; this version corrects typographical errors that appeared in
print, gives a brief update of related progress during the last two years in
the form of footnotes, and has more and updated references. (To appear in the
second edition of Essays on Mirror Manifolds.)

Algebraic Geometry;High Energy Physics - Theory;Algebraic Geometry