One application domain the mobile computing community has not yet entered is that of grid computing -- the aggregation of network-connected computers to form a large-scale, distributed system used to tackle complex scientific or commercial problems. In this paper we present the challenge of harvesting the increasingly widespread availability of Internet connected wireless mobile devices such as PDAs and laptops to be beneficially used within the emerging national and global computational grid. The integration of mobile wireless consumer devices into the Grid initially seems unlikely due to the inherent limitations typical of mobile devices, such as reduced CPU performance, small secondary storage, heightened battery consumption sensitivity, and unreliable low-bandwidth communication. However, the millions of laptops and PDAs sold annually suggest that this untapped abundance should not be prematurely dismissed. Given that the benefits of combining the resources of mobile devices with the computational grid are potentially enormous, one must compensate for the inherent limitations of these devices in order to successfully utilise them in the Grid. In this paper we identify the research challenges arising from this problem and propose our vision of a potential architectural solution. We suggest a proxy based, clustered system architecture with favourable deployment, interoperability, scalability, adaptivity, and fault-tolerance characteristics as well as an economic model to stimulate future research in this emerging field.