This thesis is divided into two parts. The rst part studies homological algebra of quasihereditary algebras, with the underlying theme being to understand properties of the Yoneda algebra of standard modules. We will rst show how homological properties of a quasi-hereditary algebra are carried over to its tensor products and wreath products. We then determine the extgroups between indecomposable standard modules of a Cubist algebra of Chuang and Turner. We will also determine generators, hence the quiver, of the Yoneda algebra of standard modules for the rhombal algebras of Peach. We also obtain a higher multiplication vanishing condition for certain rhombal algebras. The second part of this thesis studies the notion of simple-minded systems, introduced by Koenig and Liu. Such systems were designed to generate the stable module categories of artinian algebras by extension, in the same way as the sets of simple modules. We classify simple-minded systems for representation- nite self-injective algebras, and establish connections of them to various notions in combinatorics and related derived categories. We also look at the notion of simple-minded systems de ned on triangulated categories, and obtain some classi cation results using a connection between the simple-minded systems of a triangulated category and of its orbit category.