‘Borderless world’, a catch phrase promoted by Kenichi Ohmae, became highly attractive in border studies in the 1990s. Borders and political cartographies that ‘trapped’ nation-states were, for Ohmae, elements that hindered progress, economic growth, and cooperation in the globalizing market. Border studies have been a well-established research field for a long time, but a simultaneous expansion and a sort of fragmentation of the research area has occurred since the 1990s. Whereas business people, elite travellers, and prosperous tourists, for example, cross relatively soft borders regularly without difficulties, migrants and particularly asylum seekers often face the hard side of borders and bordering practices. Borders in politics are both persistent and dynamic, as an analysis of the borders in ancient Greek cities and the Roman Empire for example displays. The earlier optimism associated with the ‘borderless world’ thesis has faded for several reasons. The chapter also presents an overview of the key concepts discussed in this book.