I believe that overall we have a basic understanding of the GRB phenomenon. As usual some aspects are understood better than others.
There is a very good understanding of the afterglow. Here there are numerous observations over a wide range of wavelengths with which the theory can be confronted. The overall picture, of a slowing down relativistic flow and of synchrotron emission fit the data to a large extent (see e.g. Panaitescu and Kumar , Wijers and Galama  and many other fits of the observations to the model). We have already learned that the "cow is not spherical", namely that the relativistic flow is collimated. New observations, like those of GRB 021004 and GRb 030329, poses at times new puzzles and suggest that the basic simple picture has to be refined. It seems however, that the answers are within the scope of the current model, such as: refreshed shocks, patchy shells and variable external densities. All these phenomena are fairly reasonable in a realistic environment. Within the afterglow, I believe that the X-ray lines pose the greatest current puzzle, in terms of their energy requirements and other implications on the source (see Lazzati ). Another interesting open question is what distinguished between GHOSTs and OTGRBs - an environmental (extinction or ``improper conditions within the circum-burst matter) or an intrinsic mechanism?
The main observational challenges concerning the afterglow are the determination whether short GRBs have afterglow. A wealth of information on long GRBs arises from the information on hosts, environments and redshifts, that are determined from the afterglow observations. All these are missing for short GRBs. If short GRBs don't have afterglows, then an immediate theoretical question is why? Is it possible that they are produced in a very different environment than long ones (such as outside their original galaxies) in a region with no circum-burst matter suitable for producing the afterglow? At the moment the observational situation is not clear. The coming Swift satellite may resolve this mystery.
Another important observational question involves the search for orphan afterglows (either in radio or in optical). Their detection will establish the collimated jets picture. But even firm upper limits will set independent limits on the rates of GRBs. However, as mentioned in Section VIIK this is a very challenging observational task. This has important implication for the nature of the jets - are GRB jets standard with a fixed angular structure [219, 347, 446]? This question is related both to the overall energetics and to the rate of GRBs.
Another interesting challenge will be the resolution of the afterglow image (see Granot et al. ). This may be possible in radio for a nearby burst and the afterglow of GRB 030329 provides an excellent candidate for that. Polarization measures could pave the way for understanding of the collimation geometry and for a confirmation of the synchrotron emission process.
As we move backwards with time towards the burst we encounter the very early afterglow and the optical flash that coincides with the burst itself. Here a great progress was made with recent observations triggered by HETE II (e.g. the almost complete light curve of GRB 021004 ). SWIFT may contribute a lot to this issue. These observations could shed a light on issues like the role of pre-acceleration and neutrons that are unclear as yet. Here, I stress the importance of early and continuous radio observations, which could determine whether there are refreshed shocks during the early afterglow, that have a clear radio signature .
The understanding of the -rays emitting regions is less clear. Here, within the internal shocks model there is a reasonable understanding of the temporal structure (in terms of activity of the inner engine). However, it is not clear how is the observed spectrum produces and it seems that the simple synchrotron spectrum has to be modified (see e.g. Lloyd and Petrosian , Medvedev  for ideas on such modifications). Another possibly related puzzle is the origin of the narrow Ep distributions (see however, e.g. Daigne and Mochkovitch [67, 68], Guetta et al. ). Another set of open questions is what is the origin of the intrinsic correlation between luminosity (which in fact reflects the collimation angle [105, 291]) discovered by Fenimore and Ramirez-Ruiz  or the lag-luminosity relation discovered by Norris et al. . Similarly or even more puzzling are the implied correlations between redshift and intrinsic luminosity  and between redshift and intrinsic hardness  (note that this later correlation is essential in view of the narrow Ep distribution of GRBs). Here pairs  and IC can play an important role. Theoretical open basic physical questions that arise here (as well as in the theory of the afterglow) deal with the processes of the behavior of collisionless shocks (see e.g. Medvedev , Nikto and Medvedev , particle acceleration (see Section VB) and the generation of strong magnetic field (see ). Issues like relativistic turbulence and relativistic plasma instabilities might play an important role here (see e.g. Lyutikov and Blandford ).
From an observational point, it will be a challenge to beat the statistical power of the BATSE data in terms of number of bursts. Somewhat surprisingly, the questions what is the luminosity function of GRBs and what is the rate of GRBs as a function of redshift and to what extend GRBs follow the star formation rate are still open. Detectors with better spectral resolutions could shed some additional light on the spectrum. Another hope for new data, or at least for upper limits, arises from observational windows in higher -rays bands. On the low energy side it seems that there is a continuum between XRFs and GRBs [16, 189]. This result still has to be fully understood in the context of the narrow Ep distribution.
Looking far into the future one can hope to observe neutrinos or gravitational radiation correlated to GRBs. UHE neutrinos (Fluxes of MeV neutrinos would be too weak to be detected from cosmological distances) could confirm that protons are accelerated to UHE energies within GRBs. In turn this would proof (or disprove) the possible role of GRBs as sources of UHECRs. Gravitational radiation could give a direct clue on the activity of the inner engine (see Section VIIID4 and identify, for example, merger events.
There is a lot of observational evidence associating long GRBs with core collapse SNes. This gives a clear clue on what is the inner engine of long GRBs. There is no direct or indirect evidence on the progenitors of short GRBs. Even with this clue the situation is far from clear when we turn to the inner engine. Here most models assume some variant of a black-hole - torus system with various energy extraction mechanisms ranging from neutrino annihilation (which is less likely) to variants on the theme of electromagnetic extraction (magnetic turbulence within the accretion disk; the Blandford-Znajek mechanism which involves a disk-black hole-magnetic field interaction; pulsar like activity). Here there are open questions all around: What is the content of the ultrarelativistic flow - baryonic or Poynting flux? How is the flow accelerated and collimated? What determines the variability of the flow (required for internal shocks) and the different time scales? This part of the model seems to be in a rather poor shape - but this is understandable as we don't have any direct observations of this inner engine. One hope that arises is that there seem to be an emerging similarity between GRBs, galactic micro quasars and AGNs. All these systems accelerate collimated flows to relativistic velocities and they all seem to involve accretion onto black holes. Hopefully, this similarity could lead to a common resolution of how inner engines operate in all those systems.
I would like to thank J. Granot, D. Guetta, P. Kumar, E. Nakar and R. Sari for many helpful discussions and J. Bloom, J. Hjorth, P. Mészáros, E. Pian, K. Stanek, P. Vreeswijk and an anonymous referee for remarks. This research was supported by a grant from the US-Israel Binational Science Foundation.