This proposal deals with theoretical and computational studies of megnetoelectric couplings and related phenomena in solds.The first goal is to develop and apply first-principles methods capable to describing the full magnetoelectric response ofantiferromagnetic insulators to static fields. Previous work has successfully deal with the response associated with the spin of theelectrons, but the orbital contribution to the magnetic interaction was not included. We shall develop a framework where both spin and orbital responses are included.The second goal is to investigate the magnetoelectric coupling at optical frequencies, in an effort to explain the surprisingly large optical response that has been measured in Cr2O3. The methodologies developed for this purpose will also be used to study the natural optical activity (natural circular dichrroism) of trigonal Se and Te, with particular attention to bandstructure effects.The third goal is to develop a computational scheme based on crystalline Wannier functions to calculate accurately the orbital magnetization of metals, both spontaneous (in the case of ferromagnetes), or induced by an external perturbation (in the case ofthe magnetic shielding tensors of nonmagnetic metals).