  Typical gamma-ray burst spectra are characterized by a spectral break, Ep,
which for bright BATSE bursts is found to be narrowly clustered around 300 keV.
Recently identified X-ray flashes, which may account for a significant portion
of the whole GRB population, seem to extend the Ep distribution to a broader
range below 40 keV. Positive correlations among Ep and some other observed
parameters have been noticed. On the other hand, within the cosmological
fireball model, the issues concerning the dominant energy ingredient of the
fireball as well as the location of the GRB emission site are still unsettled,
leading to several variants of the fireball model. Here we analyze these models
within a unified framework, and critically reexamine the Ep predictions in the
various model variants. Attention is focused on the predictions of the
narrowness of the Ep distribution in different models, and the correlations
among Ep and some other measurable observables. These model properties may be
tested against the current and upcoming GRB data, through which the nature of
the fireball as well as the mechanism and site of the GRB emission will be
identified. In view of the current data, various models are appraised through a
simple Monte-Carlo simulation, and a tentative discussion about the possible
nature of X-ray flashes is presented.
