Abstract: The progresses on analyticalmodal analysis and dynamical sub-structure methods are reviewed in this paper.The classical displacement expansion theorem and the modal aggregationprinciple are discussed at the beginning of the paper. In order to acceleratethe classical method's convergence rate and to improve the efficiency of thecalculation, two new structure displacement expansion theorems areintroduced. %(High precision displacement expansion of lower order%fixed/mixed interface mode can be derived based on the new fixed/mixed%interface modal displacement expansion theorem).Corresponding to the abovethree displacements expansion theorems, three exact methods sub-structureare introduced. It is shown that all kinds ofsub-structure methods can be regarded as the variations of the above exactmethods. Therefore, systematical analytical sub-structuretechniques can be constructed based on these three theorems. It can besummarized as follows:The exact dynamic sub-structure method using the free interface mode can bederived from the free interface modal displacement expansion theorem, hencehigh precision free interface modal synthesis methods can be developed.The exact dynamic sub-structure method using the fixed mode can bederived from the fixed modal displacement expansion theorem, hencehigh precision fixed interface modal synthesis methods can be developed.The exact dynamic sub-structure method using the mixed mode can beinterfacederived from the mixed modal displacement expansion theorem, hencehigh precision mixed modal synthesis methods can be developed.These modal analysis techniques, dynamicsub-structure methods and the classical structural dynamics analysistechniques form a complete theory for the analysis of structural dynamics.