Gamma-ray bursts are the brightest explosions currently taking place in the universe. Brief, seconds to minutes long, flashes of gamma rays, they follow the formation of a black hole or highly magnetized compact object from a single collapsing massive star or from merging neutron stars. Because of the immense energy scales involved and the extremely relativistic velocities of the explosion blast wave, they provide us with a glimpse of a regime in physics inaccessible to laboratories. A feature of special interest is the `afterglow', a period of emission of increasing wavelength from X-rays to radio, which follows the original burst. This afterglow is caused by late non-thermal emission from shock-accelerated electrons in the directed blast wave as it interacts with the dilute gas surrounding the exploding system and thereby finally slows down and spreads out sideways. In this talk I will give an introduction to how afterglows are typically modelled and what a comparison between model and satellite data can tell us about the fundamental physics of the blast waves.