In this talk I will start by reviewing some results of Okounkov-Pandharipande and Bloch-Okounkov on the generating series of Gromov-Witten invariants of elliptic curves.

I will then report my recent results on this topic. These include period integral formulas for the (all-genus) n-point functions, and new combinatorial formulas of them.

If time permits, I will also mention some connections to infinite Grassmannian and integrable hierarchies.

The talk is based on my works arXiv:2304.03912 and arXiv:2310.08018.