  Since their discovery by the Beppo-SAX satellite in 1997, gamma-ray burst
afterglows have attracted an ever-growing interest. They have allowed redshift
measurements that have confirmed that gamma-ray bursts are located at
cosmological distances. Their study covers a huge range both in time (from one
minute to several months after the trigger) and energy (from the GeV to radio
domains). The purpose of this review is first to give a short historical
account of afterglow research and describe the main observational results with
a special attention to the early afterglow revealed by Swift. We then present
the standard afterglow model as it has been developed in the pre-Swift era and
show how it is challenged by the recent Swift and Fermi results. We finally
discuss different options (within the standard framework or implying a change
of paradigm) that have been proposed to solve the current problems.
