  About $39$ years ago, Kaplansky conjectured that the dimension of a
semisimple Hopf algebra over an algebraically closed field of characteristic
zero is divisible by the dimensions of its simple modules. Although it still
remains open, some partial answers to this conjecture play an important role in
classifying semisimple Hopf algebras. This paper focuses on the recent
development of Kaplansky's sixth conjecture and its applications in classifying
semisimple Hopf algebras.
