The various stages of baryonic gamma-ray burst (GRB) afterglow blast waves are reviewed. These are responsible for the afterglow emission from which much of our understanding of gamma-ray bursts derives. Initially, the blast waves are confined to the dense medium surrounding the burster (stellar envelope or dense wind), giving rise to a jet-cocoon structure. A massive ejecta is released and potentially fed by ongoing energy release from the burster and a forward–reverse shock system is set up between ejecta and ambient density. Ultimately the blast wave spreads sideways and slows down, and the dominant afterglow emission shifts from X-rays down to radio. Over the past years significant progress has been made both observationally and theoretically/numerically in our understanding of these blast waves, unique in the universe due to their often incredibly high initial Lorentz factors of 100–1000. The recent discovery of a short gamma-ray burst counterpart to a gravitational wave detection (GW 170817) brings the promise of a completely new avenue to explore and constrain the dynamics of gamma-ray burst blast waves.