The emergence and popularity of online social networks in recent years has changed the Internet ecosystem leading to a more collaborative environment. Nowadays, hundreds of millions of Internet users participate in social networks, form communities, produce and consume media content in revolutionary ways. There are very successful EU online Social Networks that account for more than 200 Mio registered users. They would benefit from working together with other relevant EU players to increase their own competitiveness and the competitiveness of the whole EU economy. A partnership among EU partners successfully active on the web (e.g. social networks, gaming, broadcasters, ICT users, incumbent ICT industry and academia) would certainly contribute to increase the competitiveness of EU industry on the web. The partnership would design measures (research, skills, regulatory, access to capital, etc.) to overcome the bottlenecks in order to increase the competitiveness of EU industry on the web. This paper focuses on the research and technological measures to be adopted. It investigates online social networks as an emerging multidisciplinary research field that bridges social science and multimedia computing. It reflects the consolidated opinion of the members of the NextMEDIA project and the Future Media Networks (FMN) cluster with the collaboration with well known experts, under the guidance of the Networked Media Systems Unit of the Information Society and Media Directorate General of the European Commission. The paper reviews the current state-of-the-art in selected aspects of social networks and presents a set of open research challenges related to online social networks. The challenges suggest that significant further research is required in the following areas: * Social graph analysis * Social media search and management * Exploiting social graphs * for predicting traffic demands and dimensioning media applications * for personalising search and recommending content * Identity algorithms * Mobile social networks * Social ranking and opinion sites * Business and social networking * Architectures for open and federated social network platforms The aforementioned fields of research challenges are only few of the dozens of research challenges that the research community faces towards the quest for a ubiquitous, intuitive and secure social web.