The magnetoelectricity of samarium iron garnet is theoretically investigated: the antiferroelectric structures of samarium ions are described and their connection with the configurations of the magnetic moments of the ions and their transformations during magnetic phase transitions is revealed. The possibility of the appearance at low temperatures of unusual Bloch domain walls, in which the magnetization vector rotates from the [uv0] axes to the [vu0] axes, which are not crystal symmetry axes, is established. The electric polarization of Bloch domain walls, which are realized both at low (T → 0 K) and high temperatures, is studied. It has been established that the electric polarization of Bloch boundaries, which arises because of an inhomogeneous magnetoelectric effect, depends significantly on their shape.