  The properties of gamma-ray bursts (GRBs) and their afterglows are used to
investigate the location of star formation activity through the history of the
Universe. This approach is motivated by the following: (i) GRBs are thought to
be associated with the deaths of massive stars and so the GRB rate ought to
follow the massive star formation rate, (ii) GRBs are the final evolutionary
phase of these short-lived stars, which do not travel far from their
birthplace, and so should be located where the stars formed, and (iii) The
differential effects of dust extinction on GRB afterglows between the X-ray and
optical wavebands can reveal whether or not large amounts of gas and dust are
present in GRB host galaxies. From recent evidence, we estimate that a
significant fraction (about 75%) of stars in the Universe formed in galaxies
that are brightest at rest-frame far-infrared (IR) wavelengths. This value is
marginally consistent with observations: 60 +/- 15% of GRBs have no detected
optical afterglow, whereas almost all have an X-ray afterglow. If the X-ray
afterglows of a large number of GRBs disappear at soft X-ray wavelengths (<2
keV), then this would provide strong evidence for dominant heavily obscured
star-formation activity. Far-IR and submillimetre studies of GRB hosts would
also test this idea: about 20% of hosts should be detectable using SCUBA.
