Abstract: Category theory is a convenient unifying language which puts into practice the following slogan. 'In order to study mathematical objects one should also consider suitable morphisms between them.' For instance, the basic language of category theory allows us to realize that seemingly different constructions arising in various fields of mathematics are instances of the same abstract notion (such as limit and colimit constructions). While being a very useful language, category theory also has its limitations. For instance in algebra and algebraic geometry one often wants to identify quasi-isomorphic chain complexes while in homotopy theory one does not want to distinguish weakly homotopy equivalent spaces. The study of such identifications and compatible constructions lies beyond the scope of category theory and it instead asks for more refined tools. During roughly the last sixty years, various alternative such tools have been proposed, and they constitute the huge field of Homotopical Algebra or Higher Category Theory. In this talk, we will give a short introduction to one such approach, namely the theory of derivators. Going back to Anderson, Franke, Grothendieck, Heller, and others (in the alphabetic order!), this approach emphasizes the calculus of derived limits and colimits. By taking a representation theoretic perspective, we also intend to shed additional light on more classical approaches.