In this talk, I will discuss the Calderón Problem with magnetic/electromagnetic perturbations in both the Riemannian and Lorentzian settings. For both of them, we consider the Laplace-Beltrami operator with lower order (electro)magnetic terms, and ask what information about the metric can be recovered when a family of Dirichlet-to-Neumann maps are given by perturbing the (electro)magnetic field. The approaches are different for the two settings: for Riemannian, we utilize the rigidity of elliptic equations to uniquely determine the metric without gauge equivalence; for Lorentzian, we rely on microlocal analysis and the propagation of singularity enjoyed by hyperbolic equations to explicitly construct the trajectory of lightlike geodesics.