Abstract: Stochastic dynamical system analysis is a highly important research area in various science and engineering fields. The probability density evolution theory provides a basis for solving key difficult issues in this area. In the present paper, some advances in the probability density evolution theory are reviewed, including the meaning and historic development of the principle of preservation of probability, the generalized density evolution equation, the dimension-reduced probability density evolution equation, and numerical methods, etc. The problems to be further studied are also pointed out.