  We introduce a relative version of the $2$-Segal simplicial spaces defined by
Dyckerhoff and Kapranov and G\'{a}lvez-Carrillo, Kock and Tonks. Examples of
relative $2$-Segal spaces include the categorified unoriented cyclic nerve,
real pseudoholomorphic polygons in almost complex manifolds and the
$\mathcal{R}_{\bullet}$-construction from Grothendieck-Witt theory. We show
that a relative $2$-Segal space defines a categorical representation of the
Hall algebra associated to the base $2$-Segal space. In this way, after
decategorification we recover a number of known constructions of Hall algebra
representations. We also describe some higher categorical interpretations of
relative $2$-Segal spaces.

Representation Theory;Category Theory;K-Theory and Homology