This chapter first presents taxonomies on approaches for resource allocation across resource sharing networks such as Grids. It then examines existing systems and classifies them under their architectures, operational models, support for the life-cycle of virtual organisations, and resource control techniques. Resource sharing networks have been established and used for various scientific applications over the last decade. The early ideas of Grid computing have foreseen a global and scalable network that would provide users with resources on demand. In spite of the extensive literature on resource allocation and scheduling across organisational boundaries, these resource sharing networks mostly work in isolation, thus contrasting with the original idea of Grid computing. Several efforts have been made towards providing architectures, mechanisms, policies and standards that may enable resource allocation across Grids. A survey and classification of these systems are relevant for the understanding of different approaches utilised for connecting resources across organisations and virtualisation techniques. In addition, a classification also sets the ground for future work on inter-operation of Grids.