Since the first article on GRBs published in 1973, almost 2000 publications have appeared in the literature [23]. Many of them have been devoted to theoretical models. By October 1993, there were 135 theoretical models [24]. It gives an idea about how puzzling the GRB problem still remains. For a more extensive overview of the models, the reader is encouraged to the excellent reviews in [15] and [25].
Some models consider a distribution of sources at a few thousands of AU, where the GRBs could be related to comets in the Oort Cloud, but Oort Cloud models cannot reproduce the homogeneity of the strong bursts without a modification of the cometary number density [26]. The energies involved would be E = 10E(28) erg in the few seconds that bursts last. No concentration or bursts towards other stars like Alpha Centauri (the nearest star to the Sun) is observed in the BATSE data [27].
During 1970s, most of the galactic models were based upon a neutron star origin in the Galactic Plane. The bursts would be caused by accretion of solid bodies (for example, comets) onto neutron stars [28-29], thermonuclear flashes [30] or starquakes [31-32]. However, the lack of concentration of the bursts towards the Galactic Plane, implies that either they are around us at 300 pc distance (and E = 10E(37) erg) or they are in the Galactic halo (E = 10E(41) erg for - 30 kpc distance), where very high velocity radiopulsars (v = 1000 km/s) born in the galactic disk, starquakes in neutron stars, unbound bursting stars, or magnetars [33] among others have been proposed as causing the GRBs.
As the Solar System is placed 8.5 kpc away from the Galactic Centre, halo models can be constrained on the basis of the symmetry of the spatial distribution of the bursts. For instance, if the bursts sources are located in the halo at 30 kpc, an asymmetry of 28 % should have been towards the Galactic Centre. The observed lack of anisotropy constrains the sources to lie at d > 150 kpc [34], i.e. in a more extended distribution than that of the dark matter in the halo (d = 8 kpc derived to the rotation curve of the Galaxy). However, since there is no excess of bursts observed towards M 31, the most massive galaxy of the Local Group the typical distance to the sources cannot much exceed 300 kpc [35-36].
Such models were first proposed in 1975 [37]. The bursts would originate in classical extragalactic sources (galaxies, quasars) or in more exotic objects, like superconducting cosmic strings or through a randomly varying focussing of radiation from distant, compact sources by gravitational lensing. Recently, other theories have been proposed, involving coalescence of neutron stars in double systems, neutron star-black hole systems [38] neutron stars-strange quark star secondaries [39], accretion induced collapse in white dwarfs [40], and ``failed'' Type I supernova [41]. The released energies would be E = 10E(51) erg (for d = 3000 Mpc) and the dominant radiation mechanisms would involve relativistic outflows of plasma [42] or somnoluminiscence [43]. The ranges for the distances (in terms of the redshifts) are: 0.2 < z < 6.0. If z < 0.2, the large superclusters of galaxies would be revealed in the distribution of the bursts. The upper limit, z < 6 has been derived from the following consideration : if GRBs are at cosmological distances, some of them would be gravitationally lensed by foreground objects [44] and a pair of bursts with similar profiles would be seen with some months of delay. So far, no such pair of identical bursts, as expected was found in a sample of 611 bursts detected by BATSE. If no positive result would be achieved in 1996-1998, it is estimated that z would be constrained to z < 1 [45]. In any case, it seems that some evolution of the sources is required in order that the models would agree with the observations [46].