This research deals with the review of former research that made to solve the challenges and complexities of both static and dynamic soil structure interaction through discussing advanced computational models and their applications and exploring methods of solving the challenges of soil structure interaction in foundation engineering to provide a guide for the engineering community through the complexes of soil structure interaction. It was found that the numerical analysis for both static and dynamic soil structure interaction using the finite element method with the aid of advanced computional models is ideal for dealing with the non-linearity of soil and structure properties and loading conditions and that the use of interface elements which is essential for idealization of forces between two different mediums and that the interaction effect of adjacent structures cannot be ignored in the seismic design of high raised buildings especially for buildings in the middle and the effect of non-linearity of soil properties can be ignored in seismic design upon increasing in soil stiffness, slenderness ratio of buildings and when the foundation soil was improved. The cost and time of dynamic soil structure analysis can be reduced by using the equivalent pier method, Mohr Columb Model in ABAQUS software, multi step and data-based method and there is a need to add guidelines on the implementation of soil structural interaction in seismic codes in order to include it in the regular design practice of structures. Moreover, it was found that the non-linearity and uncertainty of soil properties greatly affect the safety of structures and it is essential to consider static soil structure interaction analysis to assure safe and economical design of structures.