In this talk, we will give a detailed introduction to a technique of deformation of graded Hopf algebras that we introduced, in joint work with various authors, and which was successfully employed to conclude the classification of finite-dimensional pointed Hopf algebras with abelian coradical.  After a  brief historical contextualization of the subject, we shall present the aforementioned classification result and show the ideas behind the proof. Finally, we shall present the deformation algorithm, which can be also applied for other types of Hopf algebras. We shall illustrate this with examples.