This paper analyses the unstoppable phenomenon of globalisation through the lens of cyberspace. It looks at how the threats associated with this domain could evolve into a cyberwar. The paper assesses the EU’s stance on cyberspace and elaborates the directions that the EU should develop and pursue in this regard. It begins by examining the meaning of various cyber-related terms as a way of explaining the risks, threats and challenges of cyberspace. It then goes on to detail the EU’s approach to cyberspace. The paper concludes by outlining a way to increase the EU’s cyber-defence capacity and scope through the creation of an EU cyber-command that would centrally coordinate operational capacity in cyberspace in order to pursue the development of hard and offensive cyber-power. Finally, the paper also builds on the European People’s Party’s (EPP’s) call for strengthened resilience against cyberwar and offers a suggestion for an EU response to hybrid warfare and cyberwar, as outlined in the EPP’s Congress document Europe Secures Our Future.