The study of the early high-energy emission from gamma-ray bursts has been revolutionised by the Swift mission. The prompt gamma-ray emission seen by the BAT smoothly transistions into the X-ray emission seen by the XRT. In the majority of GRBs we see an initially steeply-decaying X-ray light curve, probably due to off-axis emission following termination of the most intense period of central engine activity. This phase is usually followed, within the first hour, by a shallow decay, giving the appearance of a late emission hump. The phase can last for up to a day, and hence, although faint, is energetically very significant. The energy emitted during this phase is very likely due to the forward shock being constantly refreshed by either late central engine activity or less relativistic material emitted during the prompt phase. In a significant minority of GRBs the early X-ray emission decays gradually following the prompt emission with no evidence for early temporal breaks, and in these bursts the emission may be dominated from a few hundred seconds by classical afterglow emission from the external shock as the relativistic jet is slowed by interaction with the surrounding circum-burst medium. At later times, around a day, the light curve usually steepens to resemble a pre jet-break decay, although the X-ray data do not support the occurrence of a jet break in the majority of cases. About half of the GRBs observed by Swift also show erratic X-ray flaring behaviour, usually within the first few hours although some flares are observed tip to a day or so post-trigger. Overall, the observed wide variety of early high-energy phenomena pose a major challenge to GRB models.