The theory of "point estimate" and the concept of "general convergence",which were put forward by Smale in order to investigate the complexity of algorithms for solving equations,have been producing a deep impact on the research about the local behavior,the semi-local behavior and the global behavior of iteration methods. The criterion of point estimate introduced by him not only provides a tool for quantitative analysis of the local behavior but also moti-vates the establishing of the unified determination for the semi-local behavior. Studying the global behavior in the view of discrete dynamical system will lead to many profound research subjects and open up a rich and colorful prospect. In this review,we will make a summarization about the re-search progress and some applications in nonsmooth optimi-zations.