  We severely criticize the consuetudinary analysis of the afterglows of
gamma-ray bursts (GRBs) in the conical-ejection fireball scenarios. We argue
that, instead, recent observations imply that the long-duration GRBs and their
afterglows are produced by highly relativistic jets of cannonballs (CBs)
emitted in supernova explosions. The CBs are heated by their collision with the
supernova shell. The GRB is the boosted surface radiation the CBs emit as they
reach the transparent outskirts of the shell. The exiting CBs further
decelerate by sweeping up interstellar matter (ISM). The early X-ray afterglow
is dominated by thermal bremsstrahlung from the cooling CBs, the optical
afterglow by synchrotron radiation from the ISM electrons swept up by the CBs.
We show that this model fits simply and remarkably well all the measured
optical afterglows of the 15 GRBs with known redshift, including that of GRB
990123, for which unusually prompt data are available. We demonstrate that GRB
980425 was a normal GRB produced by SN1998bw, with standard X-ray and optical
afterglows. We find that the very peculiar afterglow of GRB 970508 can be
explained if its CBs encountered a significant jump in density as they moved
through the ISM. The afterglows of the nearest 8 of the known-redshift GRBs
show various degrees of evidence for an association with a supernova akin to
SN1998bw. In all other cases such an association, even if present, would have
been undetectable with the best current photometric sensitivities. This gives
strong support to the proposition that most, maybe all, of the long-duration
GRBs are associated with supernovae. Though our emphasis is on optical
afterglows, we also provide an excellent description of X-ray afterglows.
