  Growing evidence connects the progenitor systems of the short-hard subclass
of gamma-ray bursts (GRBs) to the merger of compact object binaries composed by
two neutron stars (NSs) or by a NS and a black hole (BH). The recent
observation of the binary NS (BNS) merger event GW170817 associated with GRB
170817A brought a great deal of additional information and provided further
support to the above connection, even though the identification of this burst
as a canonical short GRB (SGRB) remains uncertain. Decades of observational
constraints and theoretical models consolidated the idea of a jet origin for
the GRB prompt emission, which can also explain the multiwavelength afterglow
radiation observed in most of the events. However, the mechanisms through which
a BNS or NS-BH merger remnant would power a collimated outflow are much less
constrained. Understanding the properties of the remnant systems and whether
they can provide the right conditions for jet production has been a main driver
of the great effort devoted to study BNS and NS-BH mergers, and still
represents a real challenge from both the physical and the computational point
of view. One fundamental open question concerns the nature of the central
engine itself. While the leading candidate system is a BH surrounded by a
massive accretion disk, the recent observation of plateau-shaped X-ray
afterglows in some SGRBs would suggest a longer-lived engine, i.e. a metastable
(or even stable) massive NS, which would also exclude NS-BH progenitors. Here
we elaborate on this key aspect, considering three different scenarios to
explain the SGRB phenomenology based on different hypotheses on the nature of
the merger remnant. Then, we discuss the basic properties of GRB 170817A and
how this event would fit within the different frameworks of the above
scenarios, under the assumption that it was or was not a canonical SGRB.
