We present some related families of orthogonal polynomials of a discrete variableand survey some of their applications in the study of (distance-regular) graphs and(completely regular) codes. One of the main peculiarities of such orthogonal systemsis their non-standard normalization condition, requiring that the square norm of eachpolynomial must equal its value at a given point of the mesh. For instance, when theyare de¯ned from the spectrum of a graph, one of these families is the system of the pre-distance polinomials which, in the case of distance-regular graphs, turns out to be thesequence of distance polinomials. The applications range from (quasi-spectral) char-acterizations of distance-regular graphs, walk-regular graphs, local distance-regularityand completely regular codes, to some results on representation theory.