The classification problem for Cuntz-Krieger algebras The classification problem for Cuntz-Krieger algebras has a long and prominent history. Indeed, Rørdam’s classification in 1995 of the simple such C*-algebras by appealing to results in symbolic dynamics paved the way for the sweeping generalization by Kirchberg and Phillips to all simple, nuclear, separable and purely infinite C*-algebras, and Restorff’s generalization in 2006 to the case of Cuntz-Krieger algebras with finitely many ideals (equivalently, of real rank zero) was a key inspiration for the recent surge in results concerning nonsimple purely infinite C*-algebras. I will explain how recent progress on the understanding of this problem - arising from the ambition to generalize Restorff's result to all unital graph C*-algebras - leads to a complete classification of the entire class of Cuntz-Krieger algebras. This is joint work with Restorff, Ruiz and Sørensen.