The theory of resurgence connects non-perturbative physics (such as instantons) to perturbative physics in a highly nontrivial way. In this talk I will concentrate on certain quantum mechanical examples where the connection can be made precise and demonstrate how the non-perturbative data can actually be decoded from the perturbative expansion. Furthermore, I will provide a geometric explanation for this relation in terms of quantization of elliptic curves. Notably, the quantum systems I will talk about are related to supersymmetric gauge theories in the Nekrasov-Shatashvili limit.