There is mounting evidence for the binary nature of the progenitors of gamma-ray bursts (GRBs). For a long GRB, the induced gravitational collapse (IGC) paradigm proposes as progenitor, or "in-state", a tight binary system composed of a carbon-oxygen core (CO core ) undergoing a supernova (SN) explosion which triggers hypercritical accretion onto a neutron star (NS) companion. For a short GRB, a NS-NS merger is traditionally adopted as the progenitor. We divide long and short GRBs into two sub-classes, depending on whether or not a black hole (BH) is formed in the merger or in the hypercritical accretion process exceeding the NS critical mass. For long bursts, when no BH is formed we have the sub-class of X-ray flashes (XRFs), with isotropic energy E iso 10 52 erg and rest-frame spectral peak energy E p,i 200 keV. When a BH is formed we have the sub-class of binary-driven hypernovae (BdHNe), with E iso 10 52 erg and E p,i 200 keV. In analogy, short bursts are similarly divided into two sub-classes. When no BH is formed, short gamma-ray flashes (S-GRFs) occur, with E iso 10 52 erg and E p,i 2 MeV. When a BH is formed, the authentic short GRBs (S-GRBs) occur, with E iso 10 52 erg and E p,i 2 MeV. We give examples and observational signatures of these four sub-classes and their rate of occurrence. From their respective rates it is possible that "in-states" of S-GRFs and S-GRBs originate from the "out-states" of XRFs. We indicate two additional progenitor systems: white dwarf-NS and BH-NS. These systems have hybrid features between long and short bursts. In the case of S-GRBs and BdHNe evidence is given of the coincidence of the onset of the high energy GeV emission with the birth of a Kerr BH.

Binary-driven-hypernovae (BdHNe) within the induced gravitational collapse (IGC) paradigm have been introduced to explain energetic (Eiso 10 52 erg), long gamma-ray bursts (GRBs) associated with type Ic supernovae (SNe). The progenitor is a tight binary composed of a carbon-oxygen (CO) core and a neutron star (NS) companion, a subclass of the newly proposed "ultra-stripped" binaries. The CO-NS short-period orbit causes the NS to accrete appriciable matter from the SN ejecta when the CO core collapses, ultimately causing it to collapse to a black hole (BH) and producing a GRB. These tight binaries evolve through the SN explosion very differently than compact binaries studied in population synthesis calculations. First, the hypercritical accretion onto the NS companion alters both the mass and momentum of the binary. Second, because the explosion timescale is on par with the orbital period, the mass ejection can not be assumed to be instantaneous. This dramatically affects the post-SN fate of the binary. Finally, the bow shock created as the accreting NS plows through the SN ejecta transfers angular momentum, braking the orbit. These systems remain bound even if a large fraction of the binary mass is lost in the explosion (well above the canonical 50% limit), and even large kicks are unlikely to unbind the system. Indeed, BdHNe produce a new family of NS-BH binaries unaccounted for in current population synthesis analyses and, although they may be rare, the fact that nearly 100% remain bound implies they may play an important role in the compact merger rate, important for gravitational waves (GWs) that, in turn, can produce a new class of ultrashort GRBs.