How do Airlines Screen Pilots?

A Germanwings flight crashed in the French Alps on March 24th while flying from Spain to Germany. The alleged reason for the tragic accident is that the copilot crashed the plane in a particularly bad instance of depression that had effected him his entire life. Many are questioning the fact that this pilot was allowed to fly a passenger jet with this mental illness, how was this problem left unknown, how did he get his job or even his license to fly passenger flights if he had had problems with severe depression?

These are all reasonable questions, and many have been answered in many news articles since the crash. The question I have not seen answered is as follows: how loose is the screening for pilots in the modern airline industry?

If this very sick man was allowed to fly a commercial jet then who else could get one of these licenses? Airline passengers go through fairly strenuous security to even travel by air but this incident has me thinking about the pilot's screening.  In the case of this flight 150 people died because the pilot made a selfish act, but what if it had been worse than selfish. It is little comfort to the families and friends of those lost, but while the pilot had control of the plane he could have taken that plane and run it into the middle of a town, or even a major city. If this man had been malicous rather than depressed then this situation could have been much worse. Should we require more screening for pilots, mentally and physically, to make sure this never happens again?