  The theory of quaternionic slice regular functions was introduced in 2006 and
successfully developed for about a decade over symmetric slice domains, which
appeared to be the natural setting for their study. Some recent articles paved
the way for a further development of the theory: namely, the study of slice
regular functions on slice domains that are not necessarily symmetric. The
present work is a panorama of geometric function theory in this new context,
where new phenomena appear. For instance, the nature of the zero sets can be
drastically different than in the symmetric case. The work includes
differential, algebraic, topological properties, as well as integral and series
representations, of slice regular functions over slice domains.
