Summary : In this colloquium we will visit some relevant combinatorial problems of the 20th century. The solution to these problems has forced to produce new ideas and to develop completely new points of view using concepts of dynamical systems theory (that is, the study of orbits of points under the action of a map). Some of these ideas are opening solutions to wide standing open problems (almost one century after their formulation). In particular, we will speak about Szemeredi's problem.