I will present some rigidity theorems about cocompact CAT(0)-spaces. For instance, I will show that if a cocompact CAT(0) space is close enough to a Euclidean space, then it is isometric to it. In the first part of the talk I will define all the objects and I will provide examples. In the second part I will sketch some proof, using a careful analysis of converging sequences of cocompact CAT(0) spaces and of the groups acting on them. The talk is partially based on joint works with Andrea Sambusetti.