We present an overview of the recent progress of applying computational geometry techniques to solve some questions, such as topology construction and broadcasting, in wireless ad hoc networks. Treating each wireless device as a node in a two-dimensional plane, we model the wireless networks by unit disk graphs in which two nodes are connected if their Euclidean distance is no more than one. We first summarize the current status of constructing sparse spanners for unit disk graphs with various combinations of the following properties: bounded stretch factor, bounded node degree, planar, and bounded total edges weight (compared with the minimum spanning tree). Instead of constructing subgraphs by removing links, we then review the algorithms for constructing a sparse backbone (connected dominating set), that is, subgraph from the subset of nodes. We then review some efficient methods for broadcasting and multicasting with theoretic guaranteed performance. Copyright © 2003 John Wiley & Sons, Ltd.