Airy beam gains a widespread concern owing to its particular properties, such as approximate nondiffraction, self-accelerating in the transverse and self-recovery as a member of nondiffraction light families. Airy beam has a broad application prospect in optoelectronics, particle manipulation, atmospheric communication and so on. The main methods of Airy beam′s propagation trajectory control are summarized. Each control principle of propagation trajectory in acceleration direction, self-bending degree, peak intensity position is analyzed. The advantages and disadvantages for each method is concluded. The research result shows that the method of controlling the peak intensity position and self-bending degree of the propagation trajectory of Airy beam by changing system parameters is simple and the system is easy to be implemented. The method based on refractive-index gradient and the special medium-nonlinear photonic crystals can reverse the direction of acceleration, but it is difficult to make it come true. The acceleration direction and intensity distribution of Airy beam′s propagation trajectory can be controlled by the special transform and it is easy to be realized.