Many European countries are still struggling with debts and debates over welfare system, such as Italy and Greece.
The European economy is now having less and less importance due to the advantages other economies have over them. For example, the Chinese and Indian market/economy, due to its large size and cheap labour, attracts most factories and many investments compared to the European market/economy. Japan, America and Korea are leaders in technology. Oil comes from the Middle East/Russia, mining resources comes from Russia, Canada, Africa and America. The European economy has less and less influence and importance, thus the many years of no growth and bankrupt countries.
With a small size (geographically speaking) and small population, it is and will be extremely hard for the European economy to improve substantially. Given the tough competitors, the difficulty is increased tenfold. The European economy is still in serious trouble.
The shared economy zone [Euro-zone] of the EU is definitely still in trouble. The UK is posting highest growth in the western world. The fact that growth in the euro-zone is still pretty much static after 6 years speaks volumes, even in significant western European countries. If that is not serious trouble what is?
With the global economy having been in such a lowly state for so long, it can be very tempting to strike up the tune of recovery with even the slightest indication that that's the case. However, in the long term I believe it's a wiser strategy to remain cautiously optimistic as we continue to strive for economic gains.
Yes, the European economy is still in serious trouble. This is not isolated to the European economy, it is economies across the world. As long as the U.S. dollar is considered the world currency, most countries will continue to feel the pain that the U.S. is going through until they begin to recover.
I say that the European economy is not in serious trouble because they unique measure of threat revolution. No financial frictions, they have positive effects on wages and employment. Although big spenders they still have high quality growth as well as trade. They are considered to rank higher than the united states.