In this article, I would like to outline the work about the correspondence between Gromov-Witten invariants and Hurwitz numbers, and concentrate mainly on the detailed study of Hirota equations for the Toda hierarchy which provides certain recurrence relations for relative Gromov-Witten invariants of P1. The papers of A. Okounkov and R. Pandharipande [11, 12] are the main sources of my study.
