Conventional dynamic systems (ab. CDS) play a very important role in studying the engineering systems and physics systems. However, much limitation exists in analyzing complex systems. Now the theory of linguistic dynamic systems (ab. LDS) is presented to deal with these systems. 1) Classification of linguistic dynamic systems According to conventional mathematical model being built or not, LDS are classified into two types: type-I LDS coming from CDS by using extension principle, type-II LDS in which fuzzy rules are advanced in place of mathematical models; 2) Computing with words (ab. CW) Computing with words is divided into three steps: the explicitation of words, constraint propagation, constraint retranslation. For different types LDS, different methods are presented to deal with computing with words. 3) the analysis of type- I LDS By using fuzzy extension principle, CDS were converted into their corresponding type-I LDS and the method of endograph is put forward to analyzing the equilibrium words, stability, bifurcation and chaos of type- I LDS. With the change of the parameter λ , the linguistic dynamics of logistic mapping Xn+1 = λXn(1-Xn),0 < λ≤4 are discussed in this paper. 4) Type-II LDS For type-II LDS, Basis words and fuzzy rule base are advanced to descript the behavior of these systems by mimicking the humans' ability to reason with and manipulate perception. In this paper, appropriate control rules are advanced to make the systems to the objective state. 5) the application of LDS in financial systems The financial system is a giant complex system. In the system, not only the numeric computation is used, but also the intelligent computation is employed. The method of computing with words is introduced in the system, and we place emphasis on discussing the stockowner yield and net worth yield.