The article discusses the physical foundations of the application of the linear magnetoelectric (ME) effect in composites for devices in the low-frequency range, including the electromechanical resonance (EMR) region. The main theoretical expressions for the ME voltage coefficients in the case of a symmetric and asymmetric composite structure in the quasi-static and resonant modes are given. The area of EMR considered here includes longitudinal, bending, longitudinal shear, and torsional modes. Explanations are given for finding the main resonant frequencies of the modes under study. Comparison of theory and experimental results for some composites is given.