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Magnetoacoustic tomography with magnetic induction (MAT-MI) is a recently introduced method for imaging electrical conductivity properties of biological tissue with high spatial resolution close to sonography. In MAT-MI the sample resides in a static magnetic field and a time-varying magnetic stimulation is applied to the sample volume. Through the action of the Lorentz force, the magnetically induced eddy current in the conductive sample causes particle vibrations and generates detectable ultrasound waves. The acoustic signal is then measured around the object to reconstruct images that are related to the object electrical conductivity distribution. The feasibility to reconstruct high spatial resolution conductivity images using MAT-MI method has been demonstrated by both computer simulation and experimental studies. Though MAT-MI technique is still in its developing stage, all the pilot studies suggest that it has potential to become a noninvasive imaging modality for high spatial resolution conductivity imaging of biological tissue and merits further investigations. This paper reviews MAT-MI about its basic theory, reconstruction algorithms and experiment studies. Some technical issues and future research directions are discussed.