Abstract: Low-thrust optimization and design of spacecraft trajectory for deep space exploration is a global optimization problem with large numbers of local solutions. The strategy of trajectory design consists of global optimization and local optimization as a whole. As a concept design, the goal of global optimization is to approximately determine exploration sequences and node times after simplifying spacecraft trajectory generated by low thrust. Local optimization is generally cataloged as direct methods, indirect methods, and hybrid methods. Direct methods convert the continuous optimal control problem into a parameter optimization problem through discretization. Indirect methods are involved in solving two- or multi-point boundary-value problems satisfying the first-order necessary conditions derived from the calculus of variations and the maximum principle. Hybrid methods partly utilize the conditions derived by indirect methods, and then as what direct methods do, resort to parameter optimization. This paper surveys the state of the art in low-thrust trajectory optimization, and describes the benefits and deficiencies of the newest and most popular methods.