Hexagonal manganites belong to an exciting class of materials exhibiting strong interactions between a highly frustrated magnetic system, the ferroelectric polarization, and the lattice. The existence and mutual interaction of different magnetic ions (Mn and rare earth) results in complex magnetic phase diagrams and novel physical phenomena. A summary and discussion of the various properties, underlying physical mechanisms, the role of the rare earth ions, and the complex interactions in multiferroic hexagonal manganites, are presented in this paper. 1. Introduction and Brief History Since the discovery of the intimate relations between electric and magnetic phenomena by Oersted, Ampère, Faraday, and others, which ultimately led James Clerk Maxwell to formulate the unified theory of electromagnetism, the mutual interaction between magnetic (electric) properties and electric (magnetic) fields has been in the focus of interest for more than a century. Wilhelm Conrad R？ntgen discovered in 1888 that a dielectric became magnetized when moving in a uniform electric field [1]. His study was motivated by the following reasoning: when a dielectric sheet, polarized in the external electric field, is moved in the direction perpendicular to the field lines, the motion of negative and positive charges, separated through the induced polarization, becomes equivalent to two electrical currents moving into opposite directions on either side of the sheet. Those currents generate a magnetic field, that is, the dielectric becomes magnetized. The experimental setup to prove the magnetoelectric effect did involve a fast rotating dielectric disc between two horizontal capacitor plates. In the same communication, R？ntgen also conjectured that the inverse effect should exist, namely the change of the polarization of a moving dielectric induced by an external magnetic field, which was indeed experimentally shown by Wilson in 1905 [2]. The possibility of a magnetoelectric effect in (non-moving) materials was later discussed by P. Curie from a symmetry point of view [3]. It took, however, many more years to understand the importance of the violation of time reversal symmetry (either by moving the dielectric, by external magnetic fields, or by magnetic orders) for the magnetoelectric coupling to become effective. The realization of the magnetoelectric effect in the antiferromagnetic phase of Cr2O3, predicted by Dzyaloshinskii [4] on symmetry grounds, was experimentally verified through the demonstration that an electric field did induce a magnetization [5–7] as well as the reverse
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