  We survey Hopf algebras and their generalizations. In particular, we compare
and contrast three well-studied generalizations (quasi-Hopf algebras, weak Hopf
algebras, and Hopf algebroids), and two newer ones (Hopf monads and hopfish
algebras). Each of these notions was originally introduced for a specific
purpose within a particular context; our discussion favors applicability to the
theory of dynamical quantum groups. Throughout the note, we provide several
definitions and examples in order to make this exposition accessible to readers
with differing backgrounds.
