  We review interaction models for GRB afterglows, with an eye on constraining
the nature of their progenitors and the geometry of explosion. Evidence is
presented for two types of progenitors. The radio afterglow of GRB 980425/SN
1998bw and the multi-frequency observations of GRB 970508 can be fitted by a
blast wave expanding into a wind-type medium, pointing to a massive star
progenitor. The broadband afterglow data of GRBs 990123 and 990510 are better
modeled by a jet expanding into a constant-density medium, implying a compact
star merger origin. Among other well observed GRBs, the jet model appears to be
more widely applicable than the wind model, although some cases are ambiguous.
The model fits often require a deviation of the energy distribution of the
radiating electrons from the commonly assumed single power-law form,
particularly for sources with a rapid decline and/or pronounced steepening in
the optical light curves. Transition to non-relativistic evolution has been
suggested as an alternative explanation for the light curve steepening,
although to produce steepening on the order of days or less would require very
high ambient densities, which are generally difficult to reconcile with radio
observations. Major open issues include the hydrodynamics of jet-ambient medium
interaction, a self-consistent determination of the electron energy
distribution, and the effects of pair production on the early afterglows which
are expected to be particularly large for the wind interaction model.
