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This paper overviews some of the theoretical and practical issues that arise in the process of developing advanced motion control systems for cooperative multiple autonomous marine vehicles (AMVs). Many of the problems addressed were formulated in the scope of the EU GREX project, entitled Coordination and Control of Cooperating Heterogeneous Unmanned Systems in Uncertain Environments. The paper offers a concise introduction to the general problem of cooperative motion control that is well rooted in illustrative mission scenarios developed collectively by the GREX partners. This is followed by the description of a general architecture for cooperative autonomous marine vehicle control in the presence of time-varying communication topologies and stringent communication constraints. The results of simulations with the NetMarSyS (Networked Marine Systems Simulator) of ISR/IST are presented and show the efficacy of the algorithms developed for cooperative motion control. The last part of the paper focuses on practical issues and describes the results of a series of tests at sea in the Azores, in the Summer of 2008. The paper concludes with a discussion of theoretical and practical implementation issues that warrant further research and development effort.