This paper introduces the cluster category, a new category derived from the bounded derived category of the module category of a finite-dimensional hereditary algebra H over a field. The cluster category is defined as a quotient of this derived category by a specific functor, and it is shown to model the combinatorics of Fomin-Zelevinsky cluster algebras in the simply-laced Dynkin case. Tilting modules in the cluster category correspond to clusters in the cluster algebra. The paper investigates the tilting theory of the cluster category, showing it is more regular than that of the module category itself and linking it to the classification of self-injective algebras of finite representation type. It also conjectures a generalization of APR-tilting. The cluster category is shown to provide a natural model for the combinatorics of cluster algebras, with connections to cluster algebras in terms of Ext-configurations and tilting objects. The paper also discusses the relationship between tilting modules and tilting objects in the cluster category, showing that basic tilting objects in the cluster category can be induced by basic tilting modules over derived equivalent algebras. The paper concludes with connections to cluster algebras, showing that the cluster category provides a framework for understanding the combinatorial structure of cluster algebras.This paper introduces the cluster category, a new category derived from the bounded derived category of the module category of a finite-dimensional hereditary algebra H over a field. The cluster category is defined as a quotient of this derived category by a specific functor, and it is shown to model the combinatorics of Fomin-Zelevinsky cluster algebras in the simply-laced Dynkin case. Tilting modules in the cluster category correspond to clusters in the cluster algebra. The paper investigates the tilting theory of the cluster category, showing it is more regular than that of the module category itself and linking it to the classification of self-injective algebras of finite representation type. It also conjectures a generalization of APR-tilting. The cluster category is shown to provide a natural model for the combinatorics of cluster algebras, with connections to cluster algebras in terms of Ext-configurations and tilting objects. The paper also discusses the relationship between tilting modules and tilting objects in the cluster category, showing that basic tilting objects in the cluster category can be induced by basic tilting modules over derived equivalent algebras. The paper concludes with connections to cluster algebras, showing that the cluster category provides a framework for understanding the combinatorial structure of cluster algebras.