We review electric dipole active magnetic resonance and nonreciprocal directional dichroism in magnetoelectric multiferroic materials in terahertz and millimeter wave regions. Owing to dynamical magnetoelectric coupling generated by the spin-dependent electric polarization, magnetic resonance, which usually occurs owing to magnetic dipole transition, can be induced by the oscillating electric fields of electromagnetic wave. This electric dipole active magnetic resonance can be useful for microscopic investigations of magnetic excitation in unconventional spin systems. The magnetoelectric coupling also induces the nonreciprocal directional dichroism, which provides a novel functionality to materials as an optical diode, in teraheltz and microwave absorption by magnetic resonance. As examples, we describe the results of the high field ESR measurements of the triangular lattice antiferromagnet CuFeO 2 and the interacting quantum spin dimer systems TlCuCl 3 and KCuCl 3.