  The X-ray light curves of hundreds of bursts are now available, thanks to the
X-ray Telescope on board the Swift satellite, on time scales from ~1 minute up
to weeks and in some cases months from the burst explosion. These data allow us
to investigate the physics of the highly relativistic fireball outflow and its
interaction with the circumburst environment. Here we review the main results
of the XRT observations, with particular regard to the evolution of the X-ray
light curves in the early phases. Unexpectedly, they are characterised by
different slopes, with a very steep decay in the first few hundred of seconds,
followed by a flatter decay and, a few thousand of seconds later, by a somewhat
steeper decay. Often strong flare activity up to few hours after the burst
explosion is also seen. These flares, most likely, are still related to the
central engine activity, that last much longer than expected and it is still
dominating the X-ray light curve well after the prompt phase, up to a few
thousand of seconds. The real afterglow emission (external shock) is dominating
the X-ray light curve only after the flatter phase ends. The flatter phase is
probably the combination of late-prompt emission and afterglow emission. When
the late-prompt emission ends the light curve steepens again. Some flare
activity can still be detected during these later phases. Finally, even the
late evolution of the XRT light curves is puzzling, in particular many of them
do not show a ``jet-break''. There are various possibilities to explain these
observations (e.g.time evolution of the microphysical parameters, structured
jet). However, a clear understanding of the formation and evolution of the jet
and of the afterglow emission is still lacking.
