A Hopf algebra is an algebra for which it is possible to form the tensor product of two representations. In order to do that, one needs an additional structure element, the so-called coproduct. In the talk, we explain more precisely what Hopf algebras are and then discuss what is known and what is not known about them. We will focus on results that generalize well-known theorems for finite groups, for example Cauchy's theorem. We will also discuss the status of a set of conjectures by I. Kaplansky about Hopf algebras.

海报