  In this review we discuss recent advances in the computation of one-point
functions in defect conformal field theories with holographic duals. We briefly
review the appearance of integrable spin chains in N=4 super Yang--Mills theory
and reformulate the problem of computing one-point functions to determining
overlaps between Bethe states and a Matrix Product State. We will then
demonstrate how these overlaps can be computed by determinant formulas. This
work is based on lectures given at the Young Researchers Integrability School
and Workshop 2018. To appear in a special issue of J. Phys. A.
