There is no true preparation for replacing a legend, but that’s what Tim Cook had to do three-and-a-half years ago following the death of Steve Jobs. Cook has led Apple so strongly, including in some surprising directions, that he has earned the No. 1 spot on Fortune’s list of the World’s Greatest Leaders. Apple’s stock has hit all-time highs, in Apple Pay and the Apple Watch the company has shown its continued appetite for innovation, and it is gradually becoming more open and outspoken, including on a variety of non-corporate social issues. By announcing that he is gay, Cook also has done something few would have predicted: become a global role model.