The morphisms between two objects in the homotopy category of a model category \(\mathcal M\) form a set (of homotopy classes). In the Dwyer-Kan simplicial localization of \(\mathcal M\) they form a simplicial set, whose set of components is the afore-mentioned set of homotopy classes. This simplicial category encodes the homotopy theoretic information of \(\mathcal M\) and can thus be thought of as its homotopy theory. Therefore, the study of the homotopy theory of homotopy theories starts with finding a model category structure on the category of simplicial categories. This is achieved in this carefully written article. The weak equivalences are the Dwyer-Kan equivalences, that is, the maps between simplicial categories inducing an equivalence of categories on \(\pi_0\) and, at the level of morphisms, weak equivalences of simplicial sets. The model category structure is in fact cofibrantly generated and right proper. Another motivation for the study of simplicial categories comes from the theory of higher categories, where they provide a model for the so-called \((\infty, 1)\)-categories. There are other models for both the homotopy theory of homotopy theories and \((\infty, 1)\)-categories, such as C. Rezk’s complete Segal spaces [Trans. Am. Math. Soc. 353, 973–1007 (2001; Zbl 0961.18008)], or Joyal’s quasi-categories. In her survey paper [J. E. Bergner, Topology 46, 397–436 (2007; Zbl 1119.55010)], the author shows that all these models are Quillen equivalent.