Radio networks are widely used today. People access voice and data services via mobile phones, Bluetooth technology replaces unhandy cables by wireless links, and wireless networking is possible via IEEE 802.11 compatible network equipment. Nodes in such networks exchange their data packets usually with fixed base stations that connect them with a wired backbone. However, in applications such as search and rescue missions or environmental monitoring, no explicit communication infrastructure may be available. In this case, the wireless hosts have to organize in a so-called wireless ad hoc network. As long as all of the hosts are within transmission range of each other, the problem of exchanging information in such a network basically boils down to designing suitable medium access control protocols, but if not all hosts can directly communicate with each other, we also need suitable routing algorithms. Designing routing algorithms for wireless ad hoc networks is an extremely challenging task and still research in progress. In this paper, we mostly focus on the simpler question of how to maintain an overlay network of wireless links between the hosts so that, as a minimum requirement, every node is reachable from every other node (i.e. the graph formed by the links is connected) as long as this is possible. Ideally, for every pair of nodes (v, w) there should also be a route from v to w with a close to minimum possible hop distance or energy consumption. The graph formed by the wireless links should also have a low degree to ensure a low maintenance cost and it should be easy to update in case of arrivals or departures of nodes or changes in their positions. This paper will present various strategies for reaching these goals under ideal as well as (more) realistic models.