  The discovery by BeppoSAX and coordinated ground-based observations of
persistent X-ray, visible and radio counterparts to GRB has successfully
concluded a search begin in 1973. The problem of explaining the mechanisms of
GRB and their persistent counterparts remains. There are two classes of models:
1) GRB continue weakly for days at all frequencies; 2) GRB emission shifts to
lower frequencies as relativistic debris sweeps up surrounding gas (in an
``external shock'') and slows. In 1) the visible afterglow is accompanied by
continuing gamma-ray emission, as hinted by the high energy emission of
GRB940217 and the ``Gang of Four'' bursts of October 27--29, 1996; the
persistent emission may fluctuate. Behavior of this sort may be found in
``internal shock'' models. Models of class 2) have been the subject of several
theoretical studies which disagree in assumptions and details but which predict
that at each frequency the flux should rise and then decline, with the maximum
coming later at lower frequencies. Some of this behavior has been observed, but
data from GRB970508 show that its afterglow cannot be simply extrapolated from
its gamma-ray emission. It is likely that both classes of processes occur in
most GRB. Comparisons between GRB show that they are not all scaled versions of
the same event. These results suggest that most gamma-ray emission is the
result of ``internal shocks'' while most afterglow is the result of ``external
shocks'', and hint at the presence of collimated outflows. Self-absorption in
the radio spectrum of GRB970508 permitted the size of the radiating surface to
be estimated, and in future GRB it may be possible to follow the expansion of
the shell in detail and to construct an energy budget.
