Recently R. Schwartz found an interesting generalization of the classical Poncelet theorem concerning the structure of the so-called Poncelet grid, the set of intersection points of the sides of a polygon inscribed into one conic and circumscribed about another conic (some of these results go back to Darboux). Based on a joint work with M. Levi, I shall explain how to obtain his result from properties of the billiard in an ellipse.