Afterglows after Swift

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.