Abstract: The main purpose of this talk is to discuss and illustrate the connection between some problems of van der Waerden type, i.e., problems of locating patterns that occur monochromatically for an arbitrary finite coloring of $\bbf{Z}$ or $\bbf{N}$, on the one hand, and topological dynamics and ergodic theory on the other hand.

The equivalence between van der Waerden's theorem and its topological version and the equivalence between the polynomial Szemeredi theorem and its ergodic version will be given.