The paper introduces a new category called the *cluster category* $\mathcal{C}$, which is obtained by quotienting the bounded derived category $\mathcal{D}$ of the module category of a finite-dimensional hereditary algebra $H$ over a field. The cluster category $\mathcal{C}$ is shown to be a natural model for the combinatorics of the Fomin–Zelevinsky cluster algebra in the simply-laced Dynkin case. The tilting theory of $\mathcal{C}$ is investigated using approximation theory, revealing that it is more regular than that of the module category and providing insights into the classification of self-injective algebras of finite representation type. The paper also conjectures a generalization of APR-tilting and explores connections between cluster categories, tilting theory, and cluster algebras. Specifically, it shows that indecomposable objects in $\mathcal{C}$ correspond to cluster variables in the cluster algebra, and that the existence of exactly two complements for almost complete basic tilting objects in $\mathcal{C}$ reflects the fact that there are exactly two ways to complete an almost complete cluster to a cluster. The paper further discusses the relationship between Ext-configurations and tilting sets, and provides a proof of a result related to exchange pairs in cluster algebras. Finally, it conjectures a link between Hom-configurations and Ext-configurations in the derived category.The paper introduces a new category called the *cluster category* $\mathcal{C}$, which is obtained by quotienting the bounded derived category $\mathcal{D}$ of the module category of a finite-dimensional hereditary algebra $H$ over a field. The cluster category $\mathcal{C}$ is shown to be a natural model for the combinatorics of the Fomin–Zelevinsky cluster algebra in the simply-laced Dynkin case. The tilting theory of $\mathcal{C}$ is investigated using approximation theory, revealing that it is more regular than that of the module category and providing insights into the classification of self-injective algebras of finite representation type. The paper also conjectures a generalization of APR-tilting and explores connections between cluster categories, tilting theory, and cluster algebras. Specifically, it shows that indecomposable objects in $\mathcal{C}$ correspond to cluster variables in the cluster algebra, and that the existence of exactly two complements for almost complete basic tilting objects in $\mathcal{C}$ reflects the fact that there are exactly two ways to complete an almost complete cluster to a cluster. The paper further discusses the relationship between Ext-configurations and tilting sets, and provides a proof of a result related to exchange pairs in cluster algebras. Finally, it conjectures a link between Hom-configurations and Ext-configurations in the derived category.