[en] A review is given of recent progress in theory of X-ray emission spectroscopy. After a general introduction, I present four topics on resonant X-ray emission spectroscopy (RXES): (1) RXES in high T_c related materials, (2) that in f⁰ and d⁰ systems, (3) that by electric quadrupole excitation, and (4) magnetic circular dichroism of RXES in ferromagnetic materials. Finally, I give some discussions on the terminology of RXES and resonant inelastic X-ray scattering (RIXS), as well as on the coherence in the second order optical process. (author)