-The present status of theoretical understanding ofthe magneto-optical Ken effect (MOKE) is reviewed. The theoretical research on MOKE has emerged from its initial stage, in which elementary ferromagnetic materials, like Fe and Ni, could be described, to a powerful first-principles electronic structure theory with which directly 'materials engineering' can be made. To illustrate this, we investigate the MOKE spectra of the following materials, which were selected because of their relevance for magneto-optical (MO) recording applications: (a) MnBi and derived compounds, (b) the natural layer systems FePt, CoPd, and CoPt, and related multilayers, (c) XPts compounds with X=V, Cr, Mn, Fe, and Co, (cl) ternary compounds related to PtMnSb, and (e) GdFe2. The ab initio calcula.ted MOKE spectra are compared to experimental spectra, if available. We predict several materials that could be promising for MO recording. We also propose a set of guidelines for the future predictions of materials having suitable MO properties.