The European Monetary Union is the first pillar within the European Union structure. In order for the EU member states to enter the euro zone and introduce the euro as their official currency, they must meet the criteria of nominal convergence (Maastricht criteria), but also the criteria of real convergence. Fulfilling the nominal convergence criteria of a particular country is bound to achieve medium and long-term fiscal stability, while real convergence criteria seek to balance the poorer and richer countries. The creation of the European Monetary Union is one of the most complex segments in European integration given the range of features that Member States had to meet. Although there are many problems in the Eurozone, it is important to point out the benefits of introducing the euro, such as: improving economic governance and cooperation of general importance, which ultimately leads to better living standards and employment growth. Although the Republic of Croatia is a member of the European Union, it still has not replaced the domestic currency with the euro. Due to the weakness of the economy, there is still a lot of room for improvement in Croatia to meet the convergence conditions that would lead to Croatia becoming the Eurosystem.