Maximum principle and the principal eigenvalue, a long story

The link between the principal eigenvalue and the maximum principle has been made very clear since the works of Protter - Weinberger, Pucci and Berestycki-Nirenberg-Varadhan. Its consequences are important and go from regularity of solutions to their very existence.
I will start by giving a survey of this rich field in the classical case of the second order uniformly elliptic operators. Then I will go on describing what and how some of these results extend or not to non linear operators and to degenerate elliptic operators.