The various stages of baryonic gamma-ray burst 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. January 8, 2018 1:34 WSPC/INSTRUCTION FILE vanEerten˙IJMPD˙review-arXiv 2 Hendrik van EertenWhat ultimately tipped the scales firmly in favor of extra-galactic models involving cataclysmic events produced by individual or merging stars, were the 1997 discoveries of afterglows and the redshift distance determinations that these made possible. 4, 5 GRB afterglows had been predicted by a class of models (most explicitly, the fireball model 6, 7 ) positing a sudden deposition of a huge amount of energy at the site of a neutron star merger or massive star collapse. This was argued to trigger an expanding relativistic blast wave, which would ultimately decelerate and produce counterpart emission at a range of frequencies (i.e. X-rays and optical, 8 radio 9 ), as the energies of shock-accelerated particles in the blast wave shifted to lower peak values. The far smaller directional error circles from afterglow X-ray and optical measurements relative to gamma rays made the first host galaxy association 10, 11 possible (GRB 970228), at which point the verdict was unambiguously in.The first detected afterglow was connected to a long GRB. It had already become clear that there existed a bimodality in the distribution of GRB durations, with separate long and short duration populations on either side of a divide at roughly 2 seconds. 12 The aforementioned host galaxy association of GRB 970228 and in particular the measurement of a supernova (SN) counterpart to nearby (uniquely so, at z = 0.0085) GRB 980425, 13 firmly established a massive star origin for the long GRBs. The predominant model for short GRBs is that these are launched during the merger of two neutron stars. 14,15 Until very recently, the peer-reviewed evidence for the short GRB scenario remained indirect, and was based on e.g. time-scale arguments, host galaxy types and measured offsets relative to host galaxies (for a recent review, see e.g. 16 ). However, shor...