A population of distant dusty galaxies emitting in the submillimetre waveba
nd has recently been detected using the Submillimetre Common-User Bolometer
Array (SCUBA) camera on the James Clerk Maxwell Telescope (JCMT). This pop
ulation can be used to trace the amount of high-redshift star formation act
ivity that is obscured from view in the optical waveband by dust, and so is
missing from existing inventories of star formation in the distant Univers
e. By including this population we can construct a complete and consistent
picture of the history of star formation. The evolution of obscured star fo
rmation at redshifts less than unity is constrained by mid- and far-infrare
d counts of dusty galaxies. Activity increases with redshift z as (1 + z)(g
amma) with gamma similar to 4, consistent with the form of evolution found
in the optical waveband by the Canada-France Redshift Survey (CFRS) to z le
ss than or similar to 1. The form of evolution at higher redshifts is const
rained by both 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 four times greater than that inf
erred from rest frame ultraviolet observations, and that a larger fraction
of this energy is emitted at high redshifts. The simplest explanation for t
hese results is that a large population of luminous, strongly obscured sour
ces at redshifts z less than or similar to 5 is missing from optical survey
s. 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 redsh
ift distribution of the detected galaxies.