Optimization problems under $(\max,\min)$-linear equation and/or inequality constraints

The paper is a survey of recent results concerning optimization problems whose set of feasible solutions is described by a finite system of so-called $(\max,\min)$-linear equations and/or inequalities. The objective function is equal to the maximum of a finite number of continuous unimodal functions $f_j\colon R\to R$ each depending on one variable $x_j\in R=(-\infty,+\infty)$. Motivation problems from the area of operations research, illustrative numerical examples, and hints for further research are included.