In 1990, Edward Luttwak coined the term ‘geoeconomics.’ He predicted that in some parts of world where the role of military power was diminishing, states would continue to compete within ‘a logic of conflict,’ but via ‘methods of commerce’ rather than military methods. In this chapter, it is argued that geoeconomical and geostrategical competition can exist at the same time, and can be mutually supportive. To illustrate this phenomenon, we will study the troubled relationship between the European Union (EU) and the Russian Federation, with particular stress on the period of the third presidency of Vladimir Putin (since May 2012).