The famous Calderón problem consists in determining the conductivity of a medium by making voltage and current measurements at
the boundary. We consider in this talk a nonlocal analog of this problem. Nonlocal operators arise in many situations where long term
interactions play a role.  The fractional Laplace is a prototype of a nonlocal operator. We will survey some of the main results on inverse problems associated with the fractional Laplacian showing that the nonlocality helps for the inverse problems.