  This is a rather personal introductory outline of an interesting class of
geometric, resp. graph- and group-theoretical structures. After an introductive
section about their genesis, the general construction of horocyclic products is
presented. Three closely related basic structures of this type are explained in
more detail: Diestel-Leader graphs, treebolic spaces, and Sol-groups, resp.
-manifolds. Emphasis is on their geometry, isometry groups, quasi-isometry
classification and boundary at infinity. Subsequently, it is clarified under
which parametrisation they admit discrete groups of isometries acting with
compact quotient. Finally, further develpoments are reviewed briefly.
  Remark: the posted version contains a correction of a misprint that appeared
on the bottom of page 22 in the version which appeared in IMN.
