Autonomous vehicles are becoming a reality. In particular, podcars were already launched in pilot projects. The wide use of such vehicles for personal transportation in urban areas is then just a matter of time and poses several research challenges and technical issues to the artificial intelligence and multiagent communities. This article focuses on issues related to the processing of demands for these vehicles and on routing them in an efficient way. An agent-based approach is proposed, which considers some variants for the processing of demands and for the routing. First, a centralized version is discussed. Then, extensions deal with decentralized routing, with enroute planning, intervehicle communication, and with a market-based approach where the manager of the service runs an auction to determine which customer to serve. All these variants aim at testing alternatives in order to shed light onto questions such as how the podcar service is to be provided and how trips have to be planned, as well as address challenges related to the management. Results show that, although this service can be provided by a central authority, communication, as well as reliability and fault-tolerance, should not be neglected.