The situation with the eurozone is a tidbit complicated if you've got no background knowledge to it, and I'm gonna go to bed in a few minutes, but the worst mistake when introducing it was imo to
introduce a common currency and therefore monetary policy, without also harmonising fiscal policy, inflation and wage development. This lead to pretty worrying divergences between north & south Europe in terms of trade balance, unit labor costs, etc., and coupled with the worst financial crisis the world has seen since the 30es and a few specific problems in some of the southern European countries (e.g. corruption, inefficient tax system, tax evasion), has created some huge problems.