This paper presents 1-D dynamic magnetization models of non-oriented soft magnetic steel sheets that can be expressed as simple systems of ordinary differential equations. The discussed models take into account the dynamic effects on magnetization due to eddy currents and hysteresis inside such sheets and differ in the way the coupled Maxwell equations with hysteresis are solved. The presented modeling approaches include finite-difference schemes of different accuracies, various magnetic equivalent circuits (MECs), including a recent approach to eliminate the deficiencies of classical MECs, and a mesh-free approach. The different modeling approaches are analyzed and compared in terms of mathematical structure, implementation work, spatial discretization, and accuracy, where both voltage- and current-driven versions are investigated.