  The purpose of this paper is twofold: first we give a survey on the recent
developments of curve counting invariants on Calabi-Yau 3-folds, e.g.
Gromov-Witten theory, Donaldson-Thomas theory and Pandharipande-Thomas theory.
Next we focus on the proof of the rationality conjecture of the generating
series of PT invariants, and discuss its conjectural Gopakumar-Vafa form.
