This thesis is mainly concerned with classification results for non-simple purely ininite C*-algebras, specifically Cuntz-Krieger algebras and graph C*-algebras, and continuous fields of Kirchberg algebras. In Article A, we perform some computations concerning projective dimension in filtrated K-theory. In joint work with Sara Arklint and Takeshi Katsura, we provide a range result complementing Gunnar Restor's classification theorem for Cuntz-Kieger algebras (Article B) and we investigate reduction of filtrated K-theory for C*-algebras of real rank zero, thereby obtaining a characterization of Cuntz-Krieger algebras with primitive ideal space of accordion type (Article C). In Article D, we establish a universal coecient theorem computing Eberhard Kirchberg's ideal-related KK-groups over a finite space for algebras with vanishing boundary maps. This result is used to classify certain continuous fields of Kirchberg algebras in Article F. A stronger result for one-parameter continuous fields is obtained in joint work with Marius Dadarlat (Article E). In Article G, we compute Stefan Schwede's n-order for certain triangulated categories of C*-algebras.