In this talk I introduce and discuss two prototypical nonlinear inverse problems, the Calderón problem and its nonlocal counterpart, the fractional Calderón problem. In these problems one seeks to recover information on an unknown conductivity or potential through indirect measurements of the generalized voltage-to-current map at the boundary/complement of a given domain. I will particularly discuss the various novel features arising from nonlocality as well as a connection between the two problems.

This is based on joint work with G. Covi, T. Ghosh, M. Salo and G. Uhlmann.