This paper presents a conjecture that the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures can be identified with the Nekrasov partition function of a certain class of N = 2 superconformal field theories (SCFTs). The authors test this conjecture at genus 0 and 1. They show that the Nekrasov partition function, which includes contributions from instantons, one-loop, and classical terms, reproduces the Liouville conformal blocks when appropriately identified with the parameters of the Liouville theory. The paper also discusses the relation between the Seiberg-Witten differential and the insertion of the energy-momentum tensor operator in the Liouville theory. The authors propose that the quantum version of the Seiberg-Witten curve can be obtained from the Liouville theory. They also consider the generalization of their results to multiple punctures on a sphere and a torus, and discuss the implications for the modular invariance of the Liouville theory. The paper concludes with a list of open problems and future directions in the study of this connection between Liouville theory and N = 2 SCFTs.This paper presents a conjecture that the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures can be identified with the Nekrasov partition function of a certain class of N = 2 superconformal field theories (SCFTs). The authors test this conjecture at genus 0 and 1. They show that the Nekrasov partition function, which includes contributions from instantons, one-loop, and classical terms, reproduces the Liouville conformal blocks when appropriately identified with the parameters of the Liouville theory. The paper also discusses the relation between the Seiberg-Witten differential and the insertion of the energy-momentum tensor operator in the Liouville theory. The authors propose that the quantum version of the Seiberg-Witten curve can be obtained from the Liouville theory. They also consider the generalization of their results to multiple punctures on a sphere and a torus, and discuss the implications for the modular invariance of the Liouville theory. The paper concludes with a list of open problems and future directions in the study of this connection between Liouville theory and N = 2 SCFTs.