Racks and quandles are binary algebraic structures arising in knot theory, representation theory of the braid groups and the study of Hopf algebras. The first part of the talk is an overview on quandle theory and the motivation behind it. The main tools used in the study of racks and quandles are group and module theory. In the second part of the talk we introduce some new ideas coming from universal algebra. In particular, we adapt the commutator theory developed by Freese and McKenzie for arbitrary algebraic structures to racks and quandles. The goal of such theory is to define the notions of abelian and central congruences, extending the familiar definitions in the setting of groups and other classical varieties in order to talk about solvable and nilpotent objects. For racks, the commutator theory has a nice and sharp interpretation in group theoretical language. We also provide some applications, both towards classification problems for finite quandles and knot theory.