Electromagnetic phenomena, such as magnetization switching, are guided by parity and time-reversal symmetries. Magnetic field and magnetization are time-odd axial vectors. Therefore, the magnetic field can switch magnetization reversibly. In contrast, the electric field is a time-even polar vector that cannot directly switch magnetization. For magnetic recording, an electrical coil-generated local magnetic field is used to switch the magnetic bit. However, in order to integrate the magnetic functionality, e.g., nonvolatile magnetic memory with high speed and low energy consumption, into the chip, it is essential to implement the magnetization switching by an electrical current, where the current induces other axial vectors through spin-transfer torque or spin–orbit torque (SOT). As an energy-efficient tool of magnetization switching, current-induced SOT has been intensively studied for the past decade, which holds great promise in the next generation of magnetic memories and magnetic logic devices [A. Manchon et al., Rev. Mod. Phys. 91, 035004 (2019); X. Han et al., Appl. Phys. Lett. 118, 120502 (2021); C. Song et al., Prog. Mater. Sci. 118, 100761 (2021); Q. Shao et al., IEEE Trans. Magn. 57, 21076639 (2021); J. Ryu et al., Adv. Mater. 32, 1907148 (2020); Y. Cao et al., iScience 23, 101614 (2020)]. In this review, we will first give the basic principle of the symmetry considerations for current-induced magnetization switching. Then, different methods to break the mirror symmetry for deterministic SOT switching will be discussed, together with examples that contain recent progress. In the end, we will give a discussion on the challenges and perspectives of the symmetry designs for SOT, which aim to inspire future fundamental studies and device applications.