This talk focuses on the analysis of N=4 SYM in the presence of a defect from the point of view of the conformal bootstrap. I will concentrate on the case in which the defect is a boundary that preserves half of the super-symmetry. After solving the constraints imposed by the symmetry preserved by the defect on correlation functions, I will present the relevant bootstrap equations. Using super-symmetry one can show that these equations possess an exact truncation leading to infinitely many algebraic constraints involving bulk and boundary CFT data. This is work in progress with Pedro Liendo.