Electrical impedance tomography (EIT) is a diffusive tomography modality in which targets are monitored using electrical boundary measurements. In EIT, an array of electrodes is attached to the surface of the target. Electric currents are injected through the electrodes and the resulting voltages between various electrode pairs are recorded. This procedure is repeated using multiple current injection patterns. The three-dimensional distribution of electrical conductivity in the target is reconstructed on the basis of these boundary measurements. The applications of EIT include medical imaging, geophysical exploration, industrial process imaging and non-destructive testing. The reconstruction problem of EIT is an ill-posed inverse problem. This implies that the solutions are non-unique and very sensitive to measurement noise and modeling errors. The solutions require either regularization of the problem (in deterministic inversion framework) or prior information on the target (in statistical framework). In this talk, the Bayesian (statistical) inversion approach to EIT is considered. Specific attention is payed to accurate modeling of measurements, modeling of uncertainties and construction of explicit statistical priors for the unknown conductivity distributions. Plenty of results from numerical simulation studies and real measurement cases are presented.