What was the level of training given to the German Fallshirmjagers compared to regular or SS troops?

Hello Indy and team! What was up with those Fallshirmjagers? It seems that no matter where you look in the European theater of war you will find German Fallshirmjagers earning serious name recognition with the Allies. When did they become such an elite fighting force and when did they earn such a level of fear and appreciation from the Allied armies? Was it as early as the landings in the Benelux or in Norway or did it come later?