Abstract: The characteristic function or the Fourier transform is a classical approach for distribution

approximation. It works well for sums of independent random variables, but it may be very dicult to

use for dependent random variables. The Stein method is a completely novel approach that works not

only for independent random variables but also for dependent random variables. It works for both

normal and non-normal approximation. It can also provide the accuracy of approximation. In this

talk we will give a brief review on fundamentals of Stein's method and recent developments in this

area. The connection between Stein's method and the Riemann hypothesis will also be discussed.