The past 20 years or so have been marked by growing consensus among researchers and policy-makers regarding the importance of innovation and institutions in economic performance. Institutions are particularly important in facilitating access to external (to the enterprise) knowledge resources in the merging open innovation paradigm. However, this function (of institutions) is both under-researched and conceptually questionable in post-socialist countries. They have embarked on a process of large-scale discontinuous change away from planned towards market economy: thus, institutions in these countries remain ‘different’ from those prevailing in advanced market economies. Within this context this chapter sets out to explore the strategies developed by enterprises operating in post-socialist institutional settings in order to access and use knowledge in the process of introducing innovation. Drawing on data from the case of Ukraine, a laggard in the transformation process, the study shows that connectedness and disconnectedness and even the concept of geographical proximity itself may be viewed very differently between (and within) different types of enterprises and regions. This has implications both for horizontal relationships with enterprises (that span global boundaries) as well the regional innovation system and its development. More specifically, the connectedness of the most radical Ukrainian innovators with Europe, and disconnectedness from the region, raises concerns about their ability to act as champions advancing the development of a strong regional system of innovation.