In this thesis we examine a few classes of geometric graphs and improve the spanning and routing ratios on these graphs. We improve the routing ratio of the Delaunay triangulation from 5.90 to 3.56. We show that it is possible to route competitively on the Theta-4 graph with a routing ratio of 17. This bound on the routing ratio also serves to improve the bound on the spanning ratio from 237 to 17. We improve the spanning ratio of the convex hull of points arranged on the surface of a sphere from approximately 12.12 to 0.999 pi, and we improve the bound on the spanning ratio of the Theta-5 graph from 9.96 to 5.70.