Spin magnetization is an important research topic in spintronics. In inversion-symmetry-broken materials, an applied electric field can not only induce a nonequilibrium spin polarization, namely the extrinsic Edelstein effect, but also generate an equilibrium magnetoelectric coupling through the renormalization of the electronic structure, namely the intrinsic Edelstein magnetoelectric effect. In centrosymmetric systems, recent studies have further proposed the emergence of second-order nonlinear Edelstein effects. By incorporating the spin degree of freedom into the quantum distance and introducing a novel Zeeman quantum geometric tensor, a unified theoretical description of spin-magnetization effects driven by dc electric fields is introduced in this perspective. In the linear-response regime, the extrinsic spin magnetization is governed by the Zeeman Berry curvature, whereas the intrinsic spin magnetization is determined by the Zeeman quantum metric. In the second-order nonlinear regime, the nonlinear Drude term and the second-order intrinsic contribution are closely related to Zeeman Berry-curvature dipole, while the second-order extrinsic magnetization is determined by the Zeeman quantum-metric dipole. Finally, we present symmetry-selection rules and candidate materials for various magnetization responses, discuss the Zeeman-quantum-geometric interpretation of dynamical spin magnetization induced by an ac electric field, and highlight the potential applications of electric-field-induced spin magnetization in Néel torque generation and electrical control of magnetic order.