In joint work with Andruskiewitsch and Vendramin we proved that over algebraically closed fields of characteristic zero, pointed Hopf algebras of odd dimension are cocycle deformations of bosonizations of Nichols algebras of diagonal type. The proof is based on deep results of several people about pointed Hopf algebras with abelian coradical, and on a new deformation argument for solvable groups. I will explain the notions in the theorem and give some details about the proof.