The paper addresses the position of peripheral areas from both a local and a global perspective. It is argued that the drive towards a network economy - often global in nature -has far reaching implications for the economic and geographical profile of border regions. The paper starts off from a theoretical perspective and shows that modern network theory - in combination with transaction cost theory - may offer a meaningful operational analytical framework for understanding the changing positions of regions in our world. A major question is then whether the new spatial dynamics will lead to convergence or divergence patterns among regions. A critical overview of convergence theories - against the background of globalisation phenomena - is then given. It is argued that there is a tendency towards club convergence. The consequences for regional development policy are next spelt out. There is no uniform policy panacea; policy strategies have to be fine-tuned and tailor-made, and should address the specific needs and opportunities of regions. Finally, the position of border regions is revisited. It is argued that accessibility polities aiming to alleviate the negative consequences of peripheral location deserve priority, provided the region has sufficient economic self-reliance to cope with competition from outside.