In this chapter we consider orthogonal dualities, i.e., we search for duality functions that satisfy an orthogonality condition in the Hilbert space weighted by the reversible measure of the process. As the standard duality functions are associated to the kernel of an intertwiner between two Lie algebra representations, here we prove that orthogonal dualities are associated to unitary intertwiners. The orthogonal dualities for the processes studied in the previous chapters turn out to be classical orthogonal polynomials which can indeed be obtained by Gram-Schmidt orthogonalization of the basic dualities.