The European Commission, like the National Science Foundation in the US and other organisations at national level, has funded the development of e-Infrastructures. Some communities in the sciences such as High Energy Physics, Astronomy and Bioinformatics have adopted the e-infrastructures and engaged in e-Science activities, whereas the social sciences and humanities lag behind. The major goal of the AVROSS study was to understand the reasons behind the low level of adoption of e-Infrastructures in the social sciences. Its main aim is to support optimisation of Grid and Géant developments, firstly by providing an analysis and assessment of the current conditions of use and to provide guidance on how e-Infrastructures may be better deployed and exploited, notably by the social sciences and humanities research communities. The study has employed the following empirical methods to meet its objectives: A survey of early adopters and enthusiasts of e-social science served to identify e-social science projects in the four fields included in the stocktaking in Europe and the US and (to some extent) beyond and a list of highly promising approaches to using e-Infrastructures. Data on the identified projects was collected through the web, as well as e-mail and phone queries to the responsible institutions. From the list of highly promising approaches eight cases were selected for the preparation of multiple case studies. These cases were described through interviews with the initiators, providers, and managers. Moreover, their potentials was assessed through small surveys of the user communities which asked for their awareness, as well as the experiences, needs, and barriers in regard to using these particular tools and approaches. Based on the results of the empirical work a set of recommendations was developed and discussed during a workshop with experts from the EU member states and industry