Magnetic resonance electrical impedance tomography (MREIT) is a new and non-invasive conductivity imaging modality, which combines the Current Density Imaging (CDI) and the traditional Electrical Impedance Tomography (EIT) techniques. MREIT, motivated to deal with the well-known ill-posed problem in the traditional EIT, has been applied to reconstruct the conductivities of human head tissues with higher accuracy and spatial resolution. This paper reviews the works of our MREIT research group in the past several years. We have developed several algorithms on imaging of head tissues including scalp, skull, brain (CSF, gray matter, white matter) with homogeneous and inhomogeneous conductivity distributions. We used RBF-MREIT, RSM-MREIT and ANFIS-MREIT algorithms to estimate the head tissue conductivities including anisotropic white matter characteristics. Furthermore, we have utilized the Two-Step MREIT algorithm and the 3-D algebraic reconstruction algorithm based on two components of the magnetic flux density to estimate inhomogeneous conductivities of human head. Simulation studies on the concentric three-spheres and realistic geometry head model demonstrated that the proposed algorithms could reconstruct the homogeneous and inhomogeneous human head tissue conductivity distributions with high resolution. Our work so far suggests that the proposed MREIT algorithms could provide useful conductivity information for solving the EEG/MEG forward/inverse problems, and merit further investigation.