Some of the first routing algorithms for geographically aware wireless networks used the Delaunay triangulation among the network's nodes as the underlying connectivity graph [4]. These solutions were considered impractical, however, because in general the Delaunay triangulation may contain arbitrarily long edges, and because calculating the Delaunay triangulation generally requires a global view of the network. Many other algorithms were then suggested for geometric routing, often assuming random placement of network nodes for analysis or simulation [30,5,31,16]. We show that, when the nodes are uniformly placed in the unit disk, the Delaunay triangulation does not contain long edges, it is easy to compute locally and it is in many ways optimal for geometric routing and flooding.In particular, we prove that, with high probability, the * Work by M.S. has been supported by a grant from the U.S.-Israeli Binational Science Foundation, by a grant from the Israel Science Fund (for a Center of Excellence in Geometric Computing), by NSF Grants CCR-97-32101, CCR-00-98246, and by the Hermann Minkowski-MINERVA Center for Geometry at Tel Aviv University.Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. maximal length of an edge in Del(P ), the Delaunay triangulation of a set P of n nodes uniformly placed in the unit disk, is O( 3 log n n ), and that the expected sum of squares of all the edges in Del(P ) is O(1). These geometric results imply that for wireless networks, randomly distributed in a unit disk (1) computing the Delaunay triangulation locally is asymptotically easy; (2) simple "face routing" through the Delaunay triangulation optimizes, up to poly-logarithmic factors, the energy load on the nodes, and (3) flooding the network, an operation quite common in sensor nets, is with high probability optimal up to a constant factor. The last property is particularly important for geocasting [20] because the Delaunay triangulation is known to be a spanner [12].