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Hybrid imaging techniques utilize couplings of physical modalities -- they are called hybrid, because, typically, the excitation and measurement quantities belong to different modalities. Recently there has been an enormous research interest in this area because these methods promise very high resolution. In this paper we give a review on hybrid tomography methods for \emph{electrical conductivity} imaging. The reviewed imaging methods utilize couplings between electric, magnetic and ultrasound modalities. By this it is possible to perform high-resolution electrical impedance imaging and to overcome the low-resolution problem of electric impedance tomography.