Some systems (in the general class nowadays known as "discrete event dynamic systems") are relevant of specific algebraic tools for their modeling. This is the realm of the so-called max-plus algebra and associated algebraic structures which allow to view those systems as "linear" systems. This story started about 25 years ago, some advances have been achieved and this talk will try to cover some of them. To relate this topic to those of this conference, one can say that a distinctive feature of such systems is that their drift is always "positive", or otherwise stated, their trajectories always "increase". This is of course reflected by the associated algebraic structures. Probably, future progress in this area depends upon our ability to understand, in this new setting, several basic facts, pertaining to algebra, geometry and analysis, which sound familiar to all of us in the classical setting we have been educated in at school.