  We give an overview of a number of Schreier-type extensions of monoids and
discuss the relation between them. We begin by discussing the characterisations
of split extensions of groups, extensions of groups with abelian kernel and
finally non-abelian group extensions. We see how these characterisations may be
immediately lifted to Schreier split extensions, special Schreier extensions
and Schreier extensions respectively. Finally, we look at weakenings of these
Schreier extensions and provide a unified account of their characterisation in
terms of relaxed actions.
