As an intelligent stochastic global optimization methodology, state transition algorithm is proposed based on the concepts of state, state transition and state space representation in modern control theory. Because of its excellent global search ability and fast convergence, state transition algorithm has been applied in various optimization problems. In this paper, firstly, it elaborates the principles and characteristics of the basic state transition algorithm systematically. Then, it illustrates the evolution and elevation of this methodology, including discrete, constrained, and multiobjective state transition algorithms, analysis and optimization of its parameters, development of state transformation operators, and related intelligent strategies, etc, Furthermore, the applications of state transition algorithm are given in terms of nonlinear system identification, industrial process control, machine learning and data ming, etc. Copyright © 2020 Acta Automatica Sinica. All rights reserved.