There have recently been calls for a more robust EU joint defense, to go so far as to have an EU military. The EU does not have a joint military- a military that is staffed and run on a supranational level.
Currently the EU member states cooperate between themselves and with outside alliances. Cooperation within the EU takes places under the Common Security and Defense Policy (CSDP) which entered into force with the Treaty of Lisbon.In addition, 22 of 28 EU member states are part of NATO.
This creates a difficult security environment, one that does not have many successes (ex: the Balkans, many African cases, almost anywhere the EU has wanted to interfere). Many states are against the idea of an supranational EU military, but others are for it. With the problems of Germany's military to the lack of 2% of GDP to their military that many NATO states don't contribute, an EU military is an alternative.
On March 8, 2015 the President of the European Commission Jean-Claude Juncker called for an EU military to help the world take the EU seriously. Further he advocated that “A common army among the Europeans would convey to Russia that we are serious about defending the values of the European Union.” His arguments also included that it would be more efficient to have a common military than each state paying to maintain it separately.
There was immediate backlash from the UK. Both the opposition and ruling party voiced their immediate displeasure with David Cameron (British Prime Minister) going so far as to say “it isn’t right for the European Union to have capabilities, armies, air forces and all the rest of it”. The next day Finland said that an EU army is "unrealistic," however the Foreign Minister said that an army composed of joint military units would be more possible. In addition, Poland, Czech Republic and Slovakia insist upon utilizing NATO rather than an EU military.
This is compared to Germany, whose defense minister stated that “our future as Europeans will one day be a European army." France has also expressed support for the idea.
Javier Solana (former NATO secretary general) and Steven Blockmans (professor at University of Amsterdam) have pointed out that the EU's treaties allow for a common military. They argue that there are political, military, and economic benefits to creating a single EU military: "Member states could achieve much more value for money than the €190 billion that they spend to keep up 28 national armies."
Where John Schindler (former National Security Agency official), argues against creating an EU army because Europe already mismanages it military forces, so pooling them is a really bad idea. Further, he argues, many defense projects are already coordinated and European-wide projects so duplicating these things is not needed.
The Bigger Picture
However, this debate is not just about having an EU military or not having one. Rather it is on the future of the EU as a Union of European States or a Union of European States. If the 28 member states of the European Union want to create a full supranational union that has political, economic, and military power they will need to move forward on creating a single European military rather than simply coordinating their military. If they want to stay as they are, with some cooperation in all areas but no real full integration, then an EU military is not needed.
As Solana and Blockmans pointed out, the EU has always been forged in crisis and the EU is facing a crisis now (think of them essentially being surrounded by conflict).
Whatever decision the EU makes on creating a military, and it is looking increasingly less and less likely, it will be a step down a road that precludes the other option (at least until another crisis or a widespread change of national governments).