Three decades after the spectroscopic detection of H
3
+
in space, the inspiring developments in physics, chemistry and astronomy of H
n
+
(
n
= 3, 5, 7) systems, which led to this Royal Society Discussion Meeting, are reviewed, the present state of the art as represented by the meeting surveyed and future lines of research considered.
This article is part of a discussion meeting issue ‘Advances in hydrogen molecular ions: H
3
+
, H
5
+
and beyond’.