The paradigm of grid computing offers interesting perspectives for future usage of computing devices. Sharing of resources makes new demanding applications feasible and helps to exploit previously unused potential. With an increasing number of mobile devices for communication and computation the vision of a mobile grid is becoming more and more attractive. Yet the transfer of the paradigm of grid computing to the domain of mobile devices is difficult. It faces multiple challenges, namely narrowness of resources, intermittent connectivity, increased heterogeneity and network dynamics. Different approaches exist to tackle isolated facets of this task. They vary in aspects of the mobile grid architecture, the kind of shared resources and the way the participants use resources and contribute resources to the grid. This chapter proposes a scheme for classifying approaches for mobile grids with respect to these aspects. Furthermore, it provides a survey of such efforts, and identifies remaining challenges and future trends.