In the talk I will present recent results on multifrequency electrical impedance tomography. The inverse problem consists in identifying a conductivity inclusion inside a homogeneous background medium by injecting one current. I will use an original spectral decomposition of the solution of the forward conductivity problem to retrieve the Cauchy data corresponding to the extreme case of perfect conductor. Considering results based on the unique continuation I will then prove the uniqueness of the multifrequency electrical impedance tomography and obtain rigorous stability estimates. Finally, I will present numerical results inspired by the developed theoretical approach. This work has been done in collaboration with Habib Ammari (ETH Zürich, Switzerland) and Chun-Hsiang Tsou (Grenoble Alpes University).