  Monogenity is a classical area of algebraic number theory that continues to
be actively researched. This paper collects the results obtained over the past
few years in this area. Several of the listed results were presented at a
series of online conferences titled "Monogenity and Power Integral Bases". We
also give a collection of the most important methods used in several of these
papers. A list of open problems for further research is also given.
