Atomic clocks are precise devices that generate time and frequency signals by exploiting the inherent oscillation frequency of atoms. They have broad applications in fields such as aerospace navigation, global positioning, and precision metrology. Laser frequency stabilization techniques are crucial for ensuring the stable operation of atomic clocks, laser frequency stability directly impacts the performance of these clocks. This review presents the working principles, characteristics, and research progress of different laser frequency stabilization techniques, including saturation absorption spectroscopy stabilization, Pound-Drever-Hall technique, and modulation transfer spectroscopy stabilization. Additionally, it provides a perspective on the future advancement of laser frequency stabilization techniques in the atomic clock filed, which integral in the development of high-performance atomic clocks.