Spin-ordered materials may exhibit a magnetic polarization which is proportional to an applied electric field and an electric polarization which is proportional to an applied magnetic field. In this paper a comprehensive discussion is given of the present knowledge of these magnetoelectric (ME) effects. The specific topics covered include the thermodynamic and magnetic symmetry considerations which are relevant to the ME effects and also to the piezomagnetic and piezomagnetoelectric effects. The major part of the paper is a review of the experimental and theoretical work on ME effects in Cr2O3 carried out by the present authors. This includes measurements of the anisotropy of the ME effects, theory of the temperature dependence and atomic mechanism of the ME effects, observation of the magnetically as well as of the electrically induced ME effect, experiments on magnetic annealing and other structure sensitive aspects of ME effects, and the role of antiferromagnetic domains in the interpretation of the results.