  We review a resistor network approach to the numerical solution of the
inverse problem of electrical impedance tomography (EIT). The networks arise in
the context of finite volume discretizations of the elliptic equation for the
electric potential, on sparse and adaptively refined grids that we call
optimal. The name refers to the fact that the grids give spectrally accurate
approximations of the Dirichlet to Neumann map, the data in EIT. The
fundamental feature of the optimal grids in inversion is that they connect the
discrete inverse problem for resistor networks to the continuum EIT problem.
