  A population of distant dusty galaxies emitting in the submillimetre waveband
has recently been detected using the Submillimetre Common-User Bolometer Array
(SCUBA) camera on the James Clerk Maxwell Telescope (JCMT). This population can
be used to trace the amount of high-redshift star-formation activity that is
obscured from view in the optical waveband by dust, and so is missing from
existing inventories of star formation in the distant Universe. By including
this population we can construct a complete and consistent picture of the
history of star formation. The evolution of obscured star formation at
redshifts less than unity is constrained by mid- and far-infrared counts of
dusty galaxies. Activity increases with redshift z as (1+z) to a power of about
4, consistent with the form of evolution found in the optical waveband by the
Canada-France Redshift Survey (CFRS) to redshifts less than about 1. The form
of evolution at higher redshifts is constrained by both our faint SCUBA counts
and the intensity of background radiation in the millimetre/submillimetre
waveband. We find that the total amount of energy emitted by dusty galaxies is
about five times greater than that inferred from restframe ultraviolet
observations, and that a larger fraction of this energy is emitted at high
redshifts. The simplest explanation for these results is that a large
population of luminous strongly-obscured sources at redshifts less than about 5
is missing from optical surveys. We discuss the possible contribution of
obscured active galactic nuclei to the submillimetre-wave background and
counts. More accurate constraints on the history of star formation will be
provided by determinations of the counts in several submillimetre wavebands and
crucially, by a reliable redshift distribution of the detected galaxies.
