We start by giving a short introduction to geometric inverse problems. Then we present our recent results regarding inverse problems for the minimal surface equation. Minimal surfaces are solutions to a quasilinear elliptic equation. We determine a minimal surface up to an isometry from the corresponding Dirichlet-to-Neumann map in dimension 2. Applications of the results include generalized boundary rigidity problem and AdS/CFT correspondence in physics. We develop nonlinear calculus for complex geometric optics solutions (CGOs) to handle numerous correction terms that appear in our analysis. The talk is based on a joint work with Catalin Carstea, Matti Lassas and Leo Tzou

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