Let G be a simple connected graph of order n and D(G) be the distance matrix of G.Suppose that λ1(D(G)) ≥ λ2(D(G)) ≥ … ≥ λn(D(G)) are the distance spectrum of G.The graph G is said to be determined by its D-spectrum if with respect to the distance matrix D(G), any graph with the same spectrum as G is isomorphic to G.In this talk, we will survey some results on the distance spectral characterization of graphs.