Magnetic materials with perpendicular magnetic anisotropy are significant for spintronics due to their potential to develop high-density magnetic memory with high thermal stability. Many methods have developed to manipulate perpendicular magnetization by electric current or electric field rather than magnetic field for realizing energy-efficient spintronics. In this review, we primarily focus on recent progress on electrical manipulation of perpendicular magnetization through spin-orbit torque and strain-mediated magnetoelectric coupling. We aim to summarize field-free switching of perpendicular magnetization and exchange bias induced by spin-orbit torque in the metallic magnetic heterostructures, spin-orbit torque switching of magnetization in the perovskite oxides, and magnetoelectric control of perpendicular magnetization mediated by piezostrain in multiferroic heterostructures. Finally, our perspectives on electrical manipulation of perpendicular magnetization by spin-orbit torque and magnetoelectric coupling are given to realize practical energy-efficient spintronic devices.