This paper introduces the special issue of the British Journal of Sociology on the subject of the transnational aspects of Olympic and world sport. The special issue is underpinned by the perspective that because sport provides a space for the forging of transnational connections and global consciousness, it is increasingly significant within contemporary processes of globalization and the making of transnational society. In this article, we examine in turn eight social scientific themes or problems that are prominent within the special issue: globalization, glocalization, neo-liberal ideologies and policies, transnational society, securitization, global civil society, transnational/global public sphere, and fantasy/imagination. We conclude by highlighting five 'circles' of future research inquiry within world sport that should be explored by social scientists.