Abstract: Most designs of the passive, active, and semi-active control to structures are carried out based on their dynamic characteristics without consideration of the soil-structure interaction (SSI) effects. However, it is known that the intensive soil-structure interaction effects for structures built on soft soil give rise to the perturbations in their dynamic characteristics. These perturbations will significantly deteriorate the effectiveness of structural vibration control. Therefore, there is a need of quantitatively including the SSI into consideration in the design of structural vibration control. Firstly, an overview is rendered in the present article on the studies of the passive, active, and semi-active control for structures considering the SSI effects. Subsequently, a comprehensive survey is given on the earthquake vibration control for asymmetric buildings with consideration of the SSI. Then the future directions of semi-active control to asymmetric buildings are proposed taking the SSI into account. Finally, the support vector machine (SVM) based semi-active control is foreground on both the elastic and inelastic asymmetric buildings including the SSI effects into consideration.