The adequate treatment of solvation effects in the calculation of UV/vis spectra is a complicated task and a general solution of this problem is still outstanding. Continuum solvation models like COSMO at least allow one to take into account a large part of the different solvent effects on electronic excitations, if the dielectric screening is properly implemented within the CI part of the underlying MO program. A comprehensive development of the respective theory is given. This ends up in a rather simple result, and it turns out that most of the former approaches to the problem have been in severe error. Geometry changes of the solute in different solvents have been taken into account for the first time and appear to be of considerable importance. A few example applications of a COSMO-MOPAC implementation are presented.