Abstract: All-electrical driven magnetization switching attracts much attention in next-generation spintronic memory and logic devices, particularly in magnetic random-access memory (MRAM) based on the spin-orbit torque (SOT), i.e. SOT-MRAM, due to its advantages of low power consumption, fast write/read speed, and improved endurance, etc. For conventional SOT-driven switching of the magnet with perpendicular magnetic anisotropy, an external assisted magnetic field is necessary to break the inversion symmetry of the magnet, which not only induces the additional power consumption but also makes the circuit more complicated. Over the last decade, significant effort has been devoted to field-free magnetization manipulation by using SOT. In this review, we introduce the basic concepts of SOT. After that, we mainly focus on several approaches to realize the field-free deterministic SOT switching of the perpendicular magnet. The mechanisms mainly include mirror symmetry breaking, chiral symmetry breaking, exchange bias, and interlayer exchange coupling. Furthermore, we show the recent progress in the study of SOT with unconventional origin and symmetry. The final section is devoted to the industrial-level approach for potential applications of field-free SOT switching in SOT-MRAM technology.