In this chapter we collect most of the restrictions on intersection arrays of distance-regular graphs known to us. (A few very basic facts have already been mentioned in §4.1D.) Some of these restrictions are important tools in the theoretical investigation of the properties of distance-regular graphs, like the unimodality of the sequence (*k*_{i})_{i} discussed in §5.1. (We already used this on several occasions.) Various bounds on the diameter in terms of the valency are theoretically important. First we have Terwilliger’s diameter bound for the case where the graph contains a quadrangle; next Ivanov’s theory, which yields abound on the diameter for arbitrary distance-regular graphs with fixed numerical girth, and finally the work by Bannai & Ito, who strive to remove the dependency on the girth from these bounds. Also Godsil proved diameter bounds, but this time in terms of a multiplicity.