European Banking Authority (EBA)
  
In the U.S., banking regulation largely falls on the Federal Reserve, though various states and other federal agencies weigh in with rules and stipulations. Europe has its web of banking regulators as well, including the European Banking Authority.
The EBA started operation in 2011 as a way of insuring the viability of the European financial system. A similar role was formerly filled by the Committee of European Banking Supervisors, but following the financial crisis of 2008, European officials launched a reorganization that eventually culminated in the creation of the EBA.
It's like if you owned a store and your security guard fell asleep, and while he was asleep, thieves tiptoed out with all your merchandise. You'd fire the guard and bring in someone else. So...the financial crisis happened, the CEBS got fired, and the EBA was brought in to make sure no one else...snuck out with the goods.
The EBA runs stress tests on banks and generally makes sure that financial institutions are able to withstand another financial crisis.