The European Union (EU) approach towards its eastern neighbourhood is a complex one as it puts emphasis on several key aspects: geopolitical, geoeconomic, security, given the problems that the European Neighbourhood Policy (ENP) is faced with and also the competition between the two important regional actors – the EU and Russia – that many times takes the form of a rivalry between spheres of influence. Firstly, this paper dwells on a brief study of the ENP eastern dimension, whereas, secondly, it focuses upon the competitive geostrategic configuration between the EU and Russia, in terms of the political and economic future of Eastern Partnership (EaP) states: Armenia, Azerbaijan, Georgia, Moldova, Ukraine and Belarus.