We briefly review the known mathematical results on uniqueness of solution in electrical impedance tomography (EIT). Generally, a real or complex conductivity is determined uniquely by complete boundary data. Uniqueness results are also known for planar resistor networks. However, it is common to make gross errors in the forward modeling of the electrical fields and this may result in no consistent solution. In particular, a two-dimensional model is often used when data are collected from a three-dimensional domain. The boundary shape is often inaccurately known, and commonly modeled by a circle. No model conductivity consistent with measured data exists when the dimension or the boundary shape is wrong.