Abstract: The author ' s main achievements in the basic theories of sand dynamics in the past three decades are summarized from the following five aspects:1) 2D and 3D dynamic effective strength criteria considering six frictional and non-frictional effects;2) a cyclic elasto-plastic model based on several new experimental findings of constitutive laws such as reversible and irreversible dilatancies;3) a constitutive theory of large post-liquefaction deformation with emphasis on the establishment of a cohesive theoretical framework consisting of mechanical laws, physical mechanisms, constitutive descriptions, numerical algorithms and pragmatic methods of prediction;4) a static and cyclic elasto-plastic model for interfaces between soils and structures, which are established based on five basic experimental laws;5) seismic earth pressure theory for rigid retaining walls and shallow-buried structures under any lateral displacement. These advances are obtained based on experimental observations, numerical simulations, mechanism analysis and theoretical description. Special attention in the present study is paid to the deep understanding of the realistic dynamic behaviours, rational descriptions of the cyclic effects of dynamic loadings induced by earthquakes, and new developments of simplified and pragmatic methods of prediction.