The main subject of this thesis is the computation of structure constants
appearing in the three-point functions for certain type of states/operators in the context of the AdS/CFT correspondence, which is one of the important parts of the dynamical problem in the dual theories of the correspondence. In the spirit of understanding this problem better, the thesis discusses the divergences appearing in the calculation of structure constants involving two giant and one point-like gravitons in
the string theories on AdS_5 x S^5 and AdS_4 x S^7/Z_k backgrounds.

Coherent state approach for the tree-level calculation of structure constants for heavy-heavy-light operators in the SU(2) x SU(2) sector of the ABJM theory is carried out both on weak and strong coupling sides of the theory.

Another remarkable determinant-result is obtained in the same sector of ABJM theory using integrability techniques for operators with precise anomalous dimensions.