  Intrinsic core generalises the finite-dimensional notion of the relative
interior to arbitrary (real) vector spaces. Our main goal is to provide a
self-contained overview of the key results pertaining to the intrinsic core and
to elucidate the relations between intrinsic core and facial structure of
convex sets in this general context. We gather several equivalent definitions
of the intrinsic core, cover much of the folklore, review relevant recent
results and present examples illustrating some of the phenomena specific to the
facial structure of infinite-dimensional sets.
