The topic of this thesis is the computation of correlation functions in defect conformal eld theories (dCFTs) that holographically dual to certain probe brane congurations. The defect eld theories discussed are all domain walls of N = 4 super Yang-Mills theory that interface between a U(N −k) gauge group and a U(N) gauge group. dCFTs may have non-trivial one-point functions and for the SO(3) × SO(3) symmetric probe D7 defect we compute one-point functions at tree-level using integrability of the N = 4 spectrum. The one-point functions are computed for SU(2)-sector operators with a small M = 0, 2, 4, 6 number of excitations and a general form for large operators is conjectured.The explicit expressions for the one-point functions shows that the matrix product state for the SO(3) × SO(3) symmetric probe D7 defect is not an integrable spin chain state. In a related setup, the probe D5 defect, we present a new solution of the boundary Yang-Baxter equation that reduces to the SO(6)-sector matrix product state for zero rapidity. Last, we consider the computation of two-point functions in the probe D5 defect for simple operators including the BMN vacuum of dierent lengths. In dCFTs the two-point functions can be expanded in conformal blocks providing a relation between the one-, two- and three-point functions.