This thesis is devoted to the study of three-point functions of $\mathcal{N}=4$ Super-Yang-Mills (SYM) theory in the planar limit by using integrability. $\mathcal{N}=4$ SYM theory is conformal invariant at quantum level and is believed to be completely solvable. By the AdS/CFT correspondence, it is dual to the type IIB superstring theory on the curved background AdS$_5\times S^5$. The three-point functions are important quantities which contain essential dynamic information of the theory. \par The necessary tools in integrability and the existing methods of computing three-point functions are reviewed. We compute the three-point functions in the higher rank $su(3)$ sector and obtain a determinant representation for one special configuration, which allows us to take the semi-classical limit. By exploring the relation between long-range interacting spin chain and inhomogeneous XXX spin chain, we develop a new approach to compute three-point functions in the $su(2)$ sector at one-loop and obtain a compact result. In the Frolov-Tseytlin limit, this result matches the result at strong coupling. \par We also explore new formulations of the three-point functions. In one formulation inspired by the light-cone string field theory, we constructed the spin vertex, which is the weak coupling counterpart of the string vertex for all sectors at tree level. Another formulation which is related to the form factor boostrap program in integrable field theory is reviewed. At weak coupling, we study the finite volume dependence of a special type of three-point functions which are related to the diagonal form factors.